Regression models form the core of the discipline of econometrics. One of the basic assumptions of classical linear regression model is that the values of the explanatory variables are fixed in repeated sampling. However, in most of the real life cases, particularly in economics the assumption of fixed regressors is not always tenable. Under a non-experimental or uncontrolled environment, the dependent variable is often under the influence of explanatory variables that are stochastic in nature. There is a huge literature related to stochastic regressors in various aspects. In this paper, a historical perspective on some of the works related to stochastic regressor is being tried to pen down based on literature search.

Education plays an essential role in the acquisition of knowledge and skills. School is the place where children’ attitudes, interests, and habits are developed. More involved and supportive a parent is towards their adolescent the higher self-esteem they will gain allowing the adolescent to feel confident and focused during school. Parents therefore enroll their children in schools that can give them expected quality of lives. The main core objective for this study was to determine the parental influence on students’ academic performance - A case study of Debre Berhan General Secondary School. A total of 118 students were included in the present study using simple random sampling technique from the total students (2367). Cross-sectional design was appropriate for this study. Primary source of data was employed collected from students. Descriptive and inferential statistics were applied. For statistical analysis SPSS 20 was used at 5% level of significance. Descriptive statistics results indicate that the average mark of students was with minimum and maximum value of 47 and 94 respectively. Multiple regression models showed that Income level, Rate of money given to satisfy basic and educational materials, Parent’s occupation, Family size, Parent’s educational level, and Parent’s way of giving motivation were found to be a significant effect on academic performance of students at 5% level of significance at study area. However, sex of students, age of students and grade level of students were not found to be significant effect to academic performance at study area. Overall model is statistically significance for the data. All the assumption of regression analysis was satisfied. Normality, Constant variance, absence of multicolinearity, linearity and absence of autocorrelation were satisfied due to formal tests and diagnostic plots. Study recommended the need for programs related to improvement of mother and father education for caring child in appropriate success of their education and also parents should allocate time to visit schools and establish good relationship and discussion about their children’s academic progress in according to way of motivation to learn actively in school.

COVID-19 was first identified in Wuhan, China in December 2019 and has caused huge death and has spread to almost all the parts of the world. There are speculation that most of the world economy and financial markets would be affected due to lockdown and social distancing. The first case of COVID-19 was first identified in Nigeria on 27th February 2020 and this study examines the effect of COVID-19 outbreak on the performance of the Nigeria stock exchange using historical data covering 2nd March 2015 to 16th April, 2020 sourced from a secondary source. This study considered the COVID-19 period from 2nd January 2020 to 16th April 2020, the results revealed a loss in stock returns and high volatility in stock returns under the COVID-19 period in Nigeria as against the normal period under study. In addition, Quadratic GARCH (QGARCH) and Exponential GARCH (EGARCH) models with dummy variable were applied to the stock returns shows that the COVID-19 has had negative effect on the stock returns in Nigeria. The study recommended that political and economic policy such as stable political environment, incentive to indigenous companies, diversification of the economy, flexible exchange rate regime be implemented so as to improve the financial market and to attract more and new investors to the Nigerian Stock Exchange.

In this paper, at first, a color image of a car is taken. Then the image is transformed into a grayscale image. After that, the motion blurring effect is applied to that image according to the image degradation model described in equation 3. The blurring effect can be controlled by a and b components of the model. Then random noise is added in the image via Matlab programming. Many methods can restore the noisy and motion blurred image; particularly in this paper Inverse filtering as well as Wiener filtering are implemented for the restoration purpose. Consequently, both motion blurred and noisy motion blurred images are restored via Inverse filtering as well as Wiener filtering techniques and the comparison is made among them.

Maximum likelihood estimation (MLE) is a popular method for parameter estimation in both applied probability and statistics but MLE cannot solve the problem of incomplete data or hidden data because it is impossible to maximize likelihood function from hidden data. Expectation maximum (EM) algorithm is a powerful mathematical tool for solving this problem if there is a relationship between hidden data and observed data. Such hinting relationship is specified by a mapping from hidden data to observed data or by a joint probability between hidden data and observed data. In other words, the relationship helps us know hidden data by surveying observed data. The essential ideology of EM is to maximize the expectation of likelihood function over observed data based on the hinting relationship instead of maximizing directly the likelihood function of hidden data. Pioneers in EM algorithm proved its convergence. As a result, EM algorithm produces parameter estimators as well as MLE does. This tutorial aims to provide explanations of EM algorithm in order to help researchers comprehend it. Moreover some improvements of EM algorithm are also proposed in the tutorial such as combination of EM and third-order convergence Newton-Raphson process, combination of EM and gradient descent method, and combination of EM and particle swarm optimization (PSO) algorithm.

The sustainability of ecotourism is the backbone of tourism development of a country. Ecotourism can contribute to both conservation and development in which involves dynamic relationship between tourism, biodiversity and communities, facilitate by great management. The purpose of this study is to analyze the dimensions of the socio-economic and environmental impacts of ecotourism in communities surrounding the Tasik Kenyir in Terengganu, Malaysia. This study provides a framework for the development and evaluation of ecotourism. The framework will determine if the relationships between indicators are positively correlated which will result in positive contribution to the other by using System Dynamic. Socio-cultural and economic data will be collected through interviews and group discussions in selected communities in Tasik Kenyir. Data on wildlife will be extracted from secondary data from Kenyir Research Institute, Universiti Malaysia Terengganu. The data analysis will explore the socio-cultural and economic differences between and within different communities due to ecotourism development, the contribution of ecotourism to conservation activities, local support for conservation and ecotourism as well as the influence of tourist activities on the distribution of wildlife species in Tasik Kenyir. This study aims to contribute toward understanding the natural resource community-ecotourism inter-relationship and help to bridge the knowledge gap that hinders biodiversity conservation initiatives. The findings will be used as a base for further development of ecotourism and will recommend alternative management options where necessary for the study area.

Inflation and exchange rates have great influence on consumer prices especially on imports and exports. Exchange rate fluctuations create inefficiency and distort world prices whereas changes in inflation rates have a direct impact on consumer goods prices which incidentally include exchange rates. There is a direct interdependence between inflation and exchange rates and this paper is aimed at investigating this relationship in dynamic context. It tries to find out how changes in inflation and exchange rates impact on another by adopting the econometric and copula approaches. Both inflation and exchange rates data are susceptible to volatility clustering, possess fat tails and are skewed coupled with conditional heteroskedasticity. Hence we model the univariate distributions by using ARMA$(p,q)$-GARCH$(x,y)$ so as to capture the most important stylized features of inflation and exchange rates. A bivariate model is then constructed by coupling the marginal distributions of inflation and exchange rates using the survival Clayton copula. Empirical results from monthly inflation and exchange rates data show positive correlation between the two based on Kendall $\tau$ test which confirms that a change in inflation results in change of exchange rates an vice versa hence there is co-movement. Furthermore, by the Granger causality test, exchange rates spikes cause changes in inflation rates. The results of the study have implications on economic policy design and hedging strategies for traders on imports and exports.

Leishmaniasis is the third most common vector-borne disease and a very important protozoan infection. Cutaneous leishmaniasis is one of the most common types of leishmaniasis infectious diseases with up to 2 million occurrences of new cases each year worldwide. A dynamic transmission multivariate time series model was applied to the data to account for overdispersion and evaluate the effects of three environmental layers as well as seasonality in the data. Furthermore, ecological niche modeling was used to investigate the geographical suitable conditions for cutaneous leishmaniasis using temperature, precipitation and altitude as environmental layers, together with the leishmaniasis presence data. A retrospective analysis of the cutaneous leishmaniasis spatial data in Afghanistan between 2003 and 2009 indicates a steady increase from 2003 to 2007, a small decrease in 2008, then another increase in 2009. An upward trend and regularly repeating patterns of highs and lows was observed related to the months of the year which suggests seasonality effect in the data. Two peaks were observed in the disease occurrence-- January to March and September to December -- which coincide with the cold period. Ecological niche modelling indicates that precipitation has the greatest contribution to the potential distribution of leishmaniasis.

A popular approach to learning about admixture from population genetic data is by computing the allele-sharing summary statistics known as f-statistics. Compared to some methods in population genetics, f-statistics are relatively simple, but interpreting them can still be complicated at times. In addition, f-statistics can be used to build admixture graphs (multi-population trees allowing for admixture events), which provide more explicit and thorough modeling capabilities but are correspondingly more complex to work with. Here, I discuss some of these issues to provide users of these tools with a basic guide for protocols and procedures. My focus is on the kinds of conclusions that can or cannot be drawn from the results of f₄-statistics and admixture graphs, illustrated with real-world examples involving human populations.

This paper has two major parts. In the first part histogram equalization for the image enhancement was implemented without using the built-in function in MATLAB. Here, at first, a color image of a rat was chosen and the image was transformed into a grayscale image. After this conversion, histogram equalization was implemented on the grayscale image. Later on, in the same image for each RGB channel, histogram equalization was implemented to observe the effect of histogram equalization on each channel. In the end, the histogram equalization was implemented to this specific color image of a rat. In the second part, for the grayscale image in part 1, the desired histogram of another colored image of a rat was introduced and histogram specification was implemented on the original colored image.

This study employed the Fully Modified Ordinary Least Squares (FMOLS) and the Error Correction Model (ECM) to investigate the long-run and short-run determinants of unemployment rate in Nigeria. To achieve this annual data on unemployment rate, inflation rate, interest rate, exchange rate and population growth from 1981 to 2016 was collected from Central Bank Statistical Bulletins and the World Bank website. The ADF test revealed that the macroeconomic variables are stationary at first difference while the Cointegration test revealed that the variables are cointegrated. Using unemployment rate as dependent variable, the FMOLS model revealed that exchange rate and population growth are positively significantly related to unemployment rate, interest rate and inflation rate were negatively related to unemployment rate but only interest rate was significant. The short run relationship revealed that the coefficient of the ecm(-1) is negative and statistically significant at 5% level indicating that the system corrects its previous period disequilibrium at the speed of 48.93% yearly. This study concludes that high exchange rate and population growth can lead to increase in unemployment rate in Nigeria while the government should develop the industrial sector and non-oil sector in order to generate employment and boost export in Nigeria.

An optimal withdrawal strategy beginning at age 65 provides a lifetime income from a portfolio, adjusted annually for inflation, while reducing the probability of living in financial ruin to an ac-ceptable level. This paper analyzes the probability of living in financial ruin, potentially for multiple years, rather than just the event of ruin. A stochastic Excel model was developed to simulate the effect of varying investment returns on a portfolio with two asset classes; large company stocks and long-term government bonds. A stochastic model is also applied to retiree mortality. The following variables were analyzed to determine their relative impact on withdrawal strategies: • Withdrawing a constant percentage of the portfolio, • Gender, • Initial asset allocation, • Asset allocation rebalancing methods, and • Low investment return environments. For both genders and most withdrawal rates, an approximately equal initial asset allocation of stocks and bonds, combined with a level rebalancing function, provided the lowest probability of living in financial ruin. Because each investment return followed its own probability distribution function, some retirees experienced financial ruin even in the most conservative simulations.

It is a common practice to detect outliers in a financial time series in order to avoid the adverse effect of additive outliers. This paper investigated the performance of GARCH family models (sGARCH; gjrGARCH; iGARCH; TGARCH and NGARCH) in the presence of different sizes of outliers (small, medium and large) for different time series lengths (250, 500, 750, 1000, 1250 and 1500) using root mean square error (RMSE) and mean absolute error (MAE) to adjudge the models. In a simulation iteration of 1000 times in R environment using rugarch package, results revealed that for small size of outliers, irrespective of the length of time series, iGARCH dominated, for medium size of outliers, it was sGARCH and gjrGARCH that dominated irrespective of time series length, while for large size of outliers, irrespective of time series length, gjrGARCH dominated. The study further leveled that in the presence of additive outliers on time series analysis, both RMSE and MAE increased as the time series length increased.

It is increasingly common for experiments in biology and medicine to involve large numbers of hypothesis tests. A natural graphical method for visualizing these tests is to construct a histogram from the p-values of these tests. In this article, we examine the shapes, both normal and abnormal, that these histograms can take on, as well as present simple inferential procedures that help to interpret the shapes in terms of diagnosing potential problems with the experiment. We examine potential causes of these problems in detail, and discuss potential remedies. Throughout, examples of abnormal-looking p-value histograms are provided and based on case studies involving real biological experiments.

The Cochran–Mantel–Haenszel (CMH) methodology is a suite of tests applicable to particular tables of count data. Inference is conditional on the treatment and outcome totals on each stratum being known before sighting the data. The CMH tests are important for analyzing randomised blocks data when the responses are categorical rather than continuous. This overview will first review the traditional CMH tests and then explore new alternative presentations of the ordinal CMH tests. Next the ordinal CMH tests will be extended so they can be used to test for higher moment effects. Finally unconditional analogues of the extended CMH tests will be developed.

There is high prevalence of hypertension and is rapidly increasing around the world, despite the intervention programme implemented, this study aimed at estimating the prevalence rate, test of association between hypertension and risk factors and model hypertension rate. Data used was obtained from the health record of Federal Medical Centre, Keffi from January 2016 – January 2019. Ordinal logistic regression model was used; Model Fitting Information, Goodness-of-Fit, Pseudo R-Square and Test of Parallel Lines are fitted to the data sets to test the accuracy and correctness of the model. The results indicated that the overall prevalence of hypertension rate is high at 36.4%, among the adult population, body mass index and gender are statistically significant, and Age is not significant in the study. Individuals that are overweight are more likely to be hypertensive compare to other weights. At age 40 – 49 years which have the highest rate of 26.5% and the odd ratio is 0.75 compared to others. One year increase in age 30 – 39, the cumulative odd of being hypertensive is 0.91 while other independent variables are held constant. The odd ratio of female being hypertensive is 0.85, therefore the females are more likely to be hypertensive with 54.4% compared to the males at 45.6% . There is no presence of multicolinearity among the variables and Logit models were formulated to calculate probabilities of the various possible outcomes.

This paper establishes methods that quantify the structure of statistical interactions within a given data set using the characterization of information theory in cohomology by finite methods, and provides their expression in terms of statistical physic and machine learning. Following [1–3], we show directly that k multivariate mutual-informations (I_k) are k-coboundaries. The k-cocycles are given by I_k = 0, which generalize statistical independence to arbitrary dimension k. The topological approach allows to investigate Shannon’s information in the multivariate case without the assumptions of independent identically distributed variables. We develop the computationally tractable subcase of simplicial information cohomology represented by entropy H_k and information I_k landscapes. The I₁ component defines a self-internal energy functional U_k, and (−1)^k I_k,k≥2 components define the contribution to a free energy functional G_k of the k-body interactions. The set of information paths in simplicial structures is in bijection with the symmetric group and random processes, provides a topological expression of the 2nd law and points toward a discrete Noether theorem (1st law). The local minima of free-energy, related to conditional information negativity and the non-Shannonian cone of Yeung [4], characterize a minimum free energy complex. This complex formalizes the minimum free-energy principle in topology, provides a definition of a complex system, and characterizes a multiplicity of local minima that quantifies the diversity observed in biology. Finite data size effects and estimation bias severely constrain the effective computation of the information topology on data, and we provide simple statistical tests for the undersampling bias and for the k-dependences following [5]. We give an example of application of these methods to genetic expression and cell-type classification. The maximal positive I_k identifies the variables that co-vary the most in the population, whereas the minimal negative I_k identifies clusters and the variables that differentiate-segregate the most. The methods unravel biologically relevant I₁₀ with a sample size of 41. It establishes generic methods to quantify the epigenetic information storage and a unified epigenetic unsupervised learning formalism.

In this work, Further properties of bornological groups are studied to find the sufficient conditions to introduce a bornology on a group. In particular, we show that every left (right) translations in bornological groups are isomorphisms and therefore the bornological group's structures are homogeneous, and this property from the bornological group is not shared with bornological semigroups. Further, the boundedness of a bornological group can be deduced from its boundedness at the identity.

Real-world time series data sets contain a combination of linear and nonlinear patterns, making the time series forecasting problem more challenging. In this paper, a new hybrid methodology is introduced for forecasting univariate time series data sets using a multiplicative error modeling approach. An autoregressive integrated moving average (ARIMA) model is combined with an autoregressive neural network (ARNN) for improving the predictions of individual forecast models. The proposed multiplicative ARIMA-ARNN model glorifies the chances of capturing the different combinations of linear and nonlinear patterns in time series. The model shows outstanding performance on six standard time-series data sets compared to other widely used single and hybrid forecasting models.

The aim of this research work was to provide model for predicting stock volatility in Nigeria Stock market. To achieve this, monthly data for Nigerian stock exchange, Exchange rate, Share index and inflation rate was collected for a period of January 1990 to December 2016.The descriptive statistics revealed these variables to exhibit volatility as a characteristics of financial time –varying series. DCC Model was fitted, were the coefficients for all the parameters and that of the correlation-Targeting (rho_21) are both negative and positive and tend very close to 1 and -1, indicating that high persistence in the conditional variances. The Model DCC, satisfied the properties of a good model of conditional mean and variance of the confidential Interval (C.I) of 1 and -1, that is, the conditional variances are finites and their series are strictly stationary. This therefore implies that the Nigerian Stock Exchange, Exchange rate, share index and Inflation rate will experience a non-steady shock in the Stock market. However Each of these variables have different length of recovery (volatility half- life) ranging from 1.5month, 6.5months, 6months to 2,4months for stock exchange, exchange rate, share index and inflation rate respectively. By implication, the volatility of these variables had a long memory, persistence and mean-reverting.

The asymmetric bimodal exponential power (ABEP) distribution is an extension of the generalized gamma distribution to the real line via adding two parameters which fit the shape of peakedness in bimodality on real line. The special values of peakedness parameters of the distribution are combination of half Laplace and half normal distributions on real line. The distribution has two parameters fitting the height of bimodality, so capacity of bimodality is enhanced by using these parameters. Adding a skewness parameter is considered to model asymmetry in data. The location-scale form of this distribution is proposed. The Fisher information matrix of these parameters in ABEP is obtained explicitly. Properties of ABEP are examined. Real data examples are given to illustrate the modelling capacity of ABEP. The replicated artificial data from maximum likelihood estimates of parameters of ABEP and distributions having an algorithm for artificial data generation procedure are provided to test the similarity with real data.

Multi-criteria decision analysis (MCDA), one of the prevalent branches of operations research, aims to design mathematical and computational tools for selecting the best alternative among several choices with respect to specific criteria. In the cloud, MCDA based online brokers uses customer specified criteria to rank different service providers. However, subjected to limited domain knowledge, the customer may exclude relevant or include irrelevant criterion, which could result in suboptimal ranking of service providers. To deal with such misspecification, this research proposes a model, which uses notion of factor analysis from the domain of unsupervised machine learning. The model is evaluated using two quality-of-service (QoS) based datasets. The first dataset i.e., feedback from customers, was compiled using leading review websites such as Cloud Hosting Reviews, Best Cloud Computing Providers, and Cloud Storage Reviews and Ratings. The second dataset i.e., feedback from servers, was generated from cloud brokerage architecture that was emulated using high performance computing (HPC) cluster at University of Luxembourg (HPC @ Uni.lu). The simulation runs in a stable cloud environment i.e. when uncertainty is low, shows that online broker (equipped with the proposed model) produces optimized ranking of service providers as compared to other brokers. This is due the fact that proposed model assigns priorities to criteria objectively (using machine learning) rather than using priorities based on subjective judgments of the customer. This research will benefit potential cloud customers that view insufficient domain knowledge as a limiting factor for acquisition of web services in the cloud.

Bayesian analysis for masked data under competing risk frameworks is studied for the purpose of assessing the impact of covariates on the hazard functions when the failure time is exactly observed for some subjects but only known to lie in an interval of time for the remaining subjects. Such data, known as partly interval-censored data, usually result from periodic inspection. Dirichlet and Gamma processes are assumed as priors for masking probabilities and baseline hazards. The Markov Chain Monte Carlo (MCMC) technique is employed for the implementation of the Bayesian approach. The effectiveness of the proposed model is tested through numerical studies, including simulated and real data sets.

NS-3 is one of the most used Network Simulators because it includes different modules, applications and protocols to simulate a wide range of network. Since new proposals usually involve a large number of simulations, a procedure to automatize the simulation process and extract statistics is very useful. "Statistical Framework" (SF) is an important module of NS-3 because it fulfills this need. SF allows us to collect simulation data and obtain statistical reports for NS-3. In this report, we present a detailed description of statistical framework module and two useful examples of its configuration.

The problem of event detection in general noisy signals arises in many applications; usually, either a functional form for the event is available, or a previous annotated sample with instances of the event that can be used to train a classification algorithm. There are situations, however, where neither functional forms nor annotated samples are available; then it is necessary to apply other strategies to separate and characterize events. In this work, we analyze 15 minute-long samples of an acoustic signal, and are interested in separating sections, or segments, of the signal which are likely to contain significative events. For that, we apply a sequential algorithm with the only assumption that an event alters the energy of the signal. The algorithm is entirely based on Bayesian methods.

COVID-19 is an infectious disease, growth of which depends upon the linked stages of the epidemic, the average number of people one person can infect and the time it takes for those people to become infectious themselves. We have studied the COVID-19 time series to understand the growth behaviour of COVID-19 cases series. A structural break occurs in the COVID-19 series at the change time form one stage to another. We have performed the structural break analysis of data available for 207 countries till April 20, 2020. There are 42 countries which have recorded five breaks in COVID cases series. This means that these countries are in the sixth stage of growth transmission and show a downward pattern in reporting in the daily cases, whereas countries with two and three breaks, record the rapid growth pattern in the daily cases. From this study, we conclude that the more the breaks in the series, there is more possibility to determine the constant or decreasing rate of daily cases. It is well fitted using lognormal distribution as this distribution is archived at its highest peak after some period and then suddenly it decreases at a longer time period. This can be seen in various countries like China, Australia, New Zealand and so on.

Fitting parameters on spline curves produces more parsimonious models, maintaining fit quality. Smoothing the splines reduces predictive variance. Individual splines are often fit by type of variable, e.g., in age-period-cohort models. Linear and cubic splines are most common. Several smoothing criteria have been used for parameter curves, with cubic splines fit by constraining the integral of splines’ squared-second derivatives popular recently. Constraining the sum of squared second differences for linear splines is analogous. Generally the degree of smoothing is selected using cross-validation. Known spline dummy-variable matrices allow regression estimation of splines, with smoothing done via constrained regression. Smoothing criteria based on sums of squares or absolute values of parameters, as in ridge regression or LASSO, improves predictive accuracy and produces splines similar to smoothing by second-derivative constraints. Variables with very low t-statistics represent points where curve-shapes barely change. Eliminating those variables leaves knots concentrated where spline shapes change. A Bayesian version of this puts shrinkage priors on spline parameters. This yields realistic joint parameter distributions, avoids problems associated with using cross-validation for parameter estimation, and readily expands to non-linear modeling, such as interactions among variable types. Regularized regression and Bayesian spline methods are compared for two example datasets.

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densities and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on different set of true values. Some real data sets were employed to show the usefulness and flexibility of the model which serves as generalization to many sub-models in the field of engineering, medical, survival and reliability analysis.

This study introduces a new discrete distribution which is a weighted version of Poisson-Lindley distribution. The weighted distribution is obtained using the negative binomial weight function and can be fitted to count data with over-dispersion. The p.m.f., p.g.f. and simulation procedure of the new weighted distribution, namely weighted negative binomial Poisson-Lindley (WNBPL), are provided. The maximum likelihood method for parameter estimation is also presented. The WNBPL distribution is fitted to several insurance datasets, and is compared to the Poisson and negative binomial distributions in terms of several statistical tests.

As the outbreak of coronavirus disease 2019 (COVID-19) is continuously increasing in India, so epidemiological modeling of COVID-19 data is urgently required for administrative strategies. Time series and is capable to predict future observations by modeling the data based on past and present data. Here, we have modeled the epidemiological COVID-19 Indian data using various models. Based on the collected COVID-19 outbreak data, we try to find the propagation rule of this outbreak disease and predict the outbreak situations in India. For India data, the time series model gives the best results in the form of predication as compared to other models for all variables of COVID-19. For new cases, new deaths, total cases and total deaths, the best fitted ARIMA models are as follows: ARIMA(0,2,3), ARIMA(0,1,1), ARIMA(0,2,0) and ARIMA(0,2,1). Based on time series analysis, we predict all variables for next month and conclude that the predictive value of Indian COVID-19 data of total cases is more than 20 lakhs with more than 43 thousand total deaths. The present chapter recommended that a comparison between various predictive models provide the accurate and better forecast value of the COVID-19 outbreak for all study variables.

Covid-19 fatality rates of 0.37% (Gangelt, Germany) and 0.17% (Santa Clara, USA) have been reported, estimated from serological studies. We show that the two confidence intervals strongly overlap when the uncertainty in the number of deaths is taken into account, so that the two investigations may be regarded as representative of the same population (tentatively: “Western society with no overload of the Health Care System during the pandemic”). Combining the results, the Covid-19 fatality rate is estimated to be found with 95% confidence in the range [0.1%; 0.3%].

The performance in terms of minimal Bayes’ error probability for detection of a high-dimensional random tensor is a fundamental under-studied difficult problem. In this work, we consider two Signal to Noise Ratio (SNR)-based detection problems of interest. Under the alternative hypothesis, i.e., for a non-zero SNR, the observed signals are either a noisy rank-R tensor admitting a Q-order Canonical Polyadic Decomposition (CPD) with large factors of size Nq  R, i.e, for 1  q  Q, where R, Nq ! ¥ with R1/q/Nq converge towards a finite constant or a noisy tensor admitting TucKer Decomposition (TKD) of multilinear (M1, . . . ,MQ)-rank with large factors of size Nq  Mq, i.e, for 1  q  Q, where Nq,Mq ! ¥ with Mq/Nq converge towards a finite constant. The detection of the random entries (coefficients) of the core tensor in the CPD/TKD is hard to study since the exact derivation of the error probability is mathematically intractable. To circumvent this technical difficulty, the Chernoff Upper Bound (CUB) for larger SNR and the Fisher information at low SNR are derived and studied, based on information geometry theory. The tightest CUB is reached for the value minimizing the error exponent, denoted by s?. In general, due to the asymmetry of the s-divergence, the Bhattacharyya Upper Bound (BUB) (that is, the Chernoff Information calculated at s? = 1/2) can not solve this problem effectively. As a consequence, we rely on a costly numerical optimization strategy to find s?. However, thanks to powerful random matrix theory tools, a simple analytical expression of s? is provided with respect to the Signal to Noise Ratio (SNR) in the two schemes considered. A main conclusion of this work is that the BUB is the tightest bound at low SNRs. This property is, however, no longer true for higher SNRs.

Upper confidence bound multi-armed bandit algorithms (UCB) typically rely on concentration in- equalities (such as Hoeffding’s inequality) for the creation of the upper confidence bound. Intu- itively, the tighter the bound is, the more likely the respective arm is or isn’t judged appropriately for selection. Hence we derive and utilise an optimal inequality. Usually the sample mean (and sometimes the sample variance) of previous rewards are the information which are used in the bounds which drive the algorithm, but intuitively the more infor- mation that taken from the previous rewards, the tighter the bound could be. Hence our inequality explicitly considers the values of each and every past reward into the upper bound expression which drives the method. We show how this UCB method fits into the broader scope of other information theoretic UCB algorithms, but unlike them is free from assumptions about the distribution of the data, We conclude by reporting some already established regret information, and give some numerical simulations to demonstrate the method’s effectiveness.

This study generalized the best copula to characterize the joint probability distribution between rainfall severity and duration in Peninsular Malaysia using two dimensional copulas. Specifically, to construct copulas, Inference Function for Margins (IFM) and Canonical Maximum Likelihood (CML) methods were specially exploited. For the purpose of achieving copula fitting, the derived rainfall variables by making use of the Standardized Precipitation Index (SPI) were fitted into several distributions. Five copulas, namely Gaussian, Clayton, Frank, Joe and Gumbel were put to the tests to establish the best data fitted copula. The tests produced acknowledged and satisfactory results of copula fitting for rainfall severity and duration. Surveying the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), only three copulas produced a better fit for parametric and semi parametric approaches. Finally, two consistency tests were conducted and the results had shown that Frank Copula produced consistent results.

The present reality of the Nigerian economy is the fact that inflation has remained unabated in spite of all exchange rate measures that have been adopted by the monetary authority. This calls for investigation into the extent to which exchange rate impact on inflation in Nigeria. The research paper examined the impact of exchange rate depreciation on inflation in Nigeria for the period 1981–2017, using Auto Regressive Distributed Lag (ARDL) Bounds Test Cointegration Procedure. The research shows that inflation rate in Nigeria is highly susceptible to lagged inflation rate, exchange rate, lagged exchange rate, lagged broad money, and lagged gross domestic product at 5% level of significance. A long run relationship was also found to exist between inflation rate, gross domestic product and general government expenditure, indicating that the model has a self-adjusting mechanism for correcting any deviation of the variables from equilibrium. Therefore, this study concludes that exchange rate is an important tool to manage inflation in the country; thus, this paper recommends that policies that have direct influence on inflation as well as exchange rate policies that would checkmate inflation movement in the country, should be used by the Central Bank of Nigeria. Also, monetary growth and import management policies should be put in place to encourage domestic production of export commodities, which are currently short-supplied. In addition, policy makers should not rely on this instrument totally to control inflation, but should use it as a complement to other macro-economic policies.

Copulas are useful tools for modeling the dependence structure between two or more variables. Copulas are becoming a quite flexible tool in modeling dependence among the components of a multivariate vector, in particular to predict losses in insurance and finance. In this article, we study the dependence structure of some well-known real life insurance data (with two components mainly) and subsequently identify the best bivariate copula to model such a scenario via VineCopula package in R. Associated structural properties of these bivariate copulas are also discussed.

Overlap coefficient (OVL) represents the proportion of overlap between two probability distributions, as a measure of the similarity between them. In this paper, we define a new overlap coefficient Λ based on KullbackLeibler divergence and compare its performance to three known overlap coefficients, namely Matusia’s Measure ρ, Morisita’s Measure λ, Weitzman’s Measure δ. We study their properties, relations between them, and give approximate expressions for the biases and the variances.

This study compared the performance of five Family Generalized Auto-Regressive Conditional Heteroscedastic (fGARCH) models (sGARCH, gjrGARCH, iGARCH, TGARCH and NGARCH) in the presence of high positive autocorrelation. To achieve this, financial time series was simulated with autocorrelated coefficients as ρ = (0.8, 0.85, 0.9, 0.95, 0.99), at different time series lengths (as 250, 500, 750, 1000, 1250, 1500) and each trial was repeated 1000 times carried out in R environment using rugarch package. And the performance of the preferred model was judged using Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). Results from the simulation revealed that these GARCH models performances varies with the different autocorrelation values and at different time series lengths. But in the overall, NGARCH model dominates with 62.5% and 59.3% using RMSE and MAE respectively. We therefore recommended that investors, financial analysts and researchers interested in stock prices and asset return should adapt NGARCH model when there is high positive autocorrelation in the financial time series data.

Cardiovascular disease is the number one cause of death in the world and Quoting from WHO, around 31% of deaths in the world are caused by cardiovascular diseases and more than 75% of deaths occur in developing countries. The results of patients with cardiovascular disease produce many medical records that can be used for further patient management. This study aims to develop a method of data mining by grouping patients with cardiovascular disease to determine the level of patient complications in the two clusters. The method applied is principal component analysis (PCA) which aims to reduce the dimensions of the large data available and the techniques of data mining in the form of cluster analysis which implements the K-Medoids algorithm. The results of data reduction with PCA resulted in five new components with a cumulative proportion variance of 0.8311. The five new components are implemented for cluster formation using the K-Medoids algorithm which results in the form of two clusters with a silhouette coefficient of 0.35. Combination of techniques of Data reduction by PCA and the application of the K-Medoids clustering algorithm are new ways for grouping data of patients with cardiovascular disease based on the level of patient complications in each cluster of data generated.

This paper considers a non-mixture cure model for right censored data. It utilizes the maximum likelihood method to estimate model parameters in the non-mixture cure model. The simulation study is based on Fréchet susceptible distribution to evaluate the performance of the method. Comparing with Weibull and exponentiated exponential distributions, the non-mixture Fréchet distribution is shown to be the best in modeling a real data on allogeneic marrow HLA-matched donors and ECOG phase III clinical trial e1684 data.

Research background: Relationship between inflation rate, unemployment rate, interest rate and real gross domestic product per capita in Nigeria. However, there seems to be a short-run or long-run relationship among the macroeconomic variables.Purpose: This study investigated the impact of the inflation rate, unemployment rate and interest rate on real gross domestic product per capita (RGDPPC) (proxy for economic growth) and proffered recommendations towards enhancing economic growth and to reduce the distasteful effects of inflation rate, unemployment rate and interest rate in Nigeria in this present time economic challenges.Research methodology: This study applied a linear dynamic model Autoregressive Distributed Lag (ARDL) modeling technique to analyze the short-run dynamics and long-run relationship of the economic growth in Nigeria over the sample period between 1984 and 2017 using annual secondary data extracted from World Bank Development Indicators Report (last updated January 2019).Results: The empirical results showed that there was long-run relationship between inflation rate, unemployment rate and interest rate on real gross domestic product per capita (proxy for economic growth) in Nigeria. The result further revealed that only unemployment rate had a significant positive impact on real gross domestic product per capita in the long-run and inflation rate had a significant negative impact on real gross domestic product per capita in the short-run.Novelty: Therefore, the study concluded that unemployment rate and inflation rate proved to have significant impacts on economic growth in the long-run and short-run respectively. Formulation of policies to reduce unemployment through the adoption of labour concentrated technique of production, entrepreneurship development and policy to keep the inflation rate at single digit.

The very first case of corona-virus illness was recorded on 30 January 2020, in India and the number of infected cases, including the death toll, continues to rise. In this paper, we present short-term forecasts of COVID-19 for 28 Indian states and five union territories using real-time data from 30 January to 20May 2020. Applying Holt’s second-order exponential smoothing method and autoregressive integrated moving average (ARIMA) model, we generated 10-day ahead forecasts of the likely number of infected cases and deaths in India until 29 May2020. Our results show that the number of cumulative cases in India will rise to169109 [PI 95% (14426, 19455)], concurrently the number of deaths may increase to 4863 [PI 95% (4221, 5551)] by 29 May 2020.Further, we have marked the states (e.g. Delhi, Uttar Pradesh, Rajasthan, Madhya Pradesh, Maharashtra, Gujarat, and Tamil Nadu) where outburst is expected by considering the cases above three standard deviations. Under the worst-case scenario, Maharashtra is likely to be the most affected state with around 62628 [PI 95% (52840, 73555)] cumulative cases by 29 May 2020. However, Kerala and Karnataka are likely to remain in the lesser affected region. The presented results mark the states where lockdown by 1 June2020, can be loosened.

The chain ladder method is a popular technique to estimate the future reserves needed to handle claims that are not fully settled. Since the predictions of the aggregate portfolio (consisting of different subportfolios) in general differ from the sum of the predictions of the subportfolios, a general multivariate chain ladder (GMCL) method has already been proposed. However, the GMCL method is based on the seemingly unrelated regression (SUR) technique which makes it very sensitive to outliers. To address this issue a robust alternative is introduced which estimates the SUR parameters in a more outlier resistant way. With the robust methodology it is possible to detect which claims have an abnormally large influence on the reserve estimates. We introduce a simulation design to generate artificial multivariate run-off triangles based on the GMCL model and illustrate the importance of taking into account contemporaneous correlations and structural connections between the run-off triangles. By adding contamination to these artificial datasets, the sensitivity of the traditional GMCL method and the good performance of the robust GMCL method is shown. From the analysis of a portfolio from practice it is clear that the robust GMCL method can provide better insight in the structure of the data.

This study investigates the impact of global financial crisis and the present COVID-19 pandemic on daily and weekly Crude oil futures using four variants of ARMA-GARCH models: ARMA-sGARCH, ARMA-eGARCH, ARMA-TGARCH and ARMA- aPARCH with dummy variables We also investigated the persistence, half-life and backtesting of the models. This study therefore seeks to contribute to the body of literature on the impact of global financial crisis and the present COVID-19 pandemic on crude oil futures market. This investigation of the impact of global financial crisis and the COVID-19 on crude oil futures has not been much studied at present. We obtained and analyzed the daily and weekly crude oil futures from secondary sources. Daily crude oil futures used in this study covers the period from the 4th January 2000 to 27th April 2020 while the weekly crude oil futures covered from 2ndJanuary 2000 to 26th April 2020 . The global financial crisis period covered from 2nd July 2007 to 31st March 2009 and the current COVID-19 pandemic covered from 1st January 2020 to 27th April, 2020. The study used both student t and skewed student t innovations with AIC, goodness-of-test fit and backtesting to select the best model. Most of the estimated ARMA-GARCH models are supported by skewed student t distribution while most of the ARMA-GARCH models exhibited high persistence values in the presence of global financial crisis and the COVID-19 pandemic. In the overall, the estimated ARMA(1,0)-eGARCH(2,1) and ARMA(1,0)-eGARCH(2,2) model for daily crude oil futures and weekly crude oil futures respectively have been significantly impacted by the global financial crisis and the Present COVID-19 pandemic while the preferred estimated models also passed the goodness-of-test fit and backtesting.This study recommends shareholders and investors should think outside the box as crude oil futures tend to be affected by global financial crisis and COVID-19 pandemic while countries also that depend mostly on crude oil are encouraged to diversify their economy in other to survive and be sustained during financial and health crisis.

Dynamic hedging has been adopted by many insurance companies to mitigate the financial risks associated with variable annuity guarantees. In order to simulate the performance of dynamic hedging for variable annuity products, insurance companies rely on nested stochastic projections, which is highly computationally intensive and often prohibitive for large variable annuity portfolios. Metamodeling techniques have recently been proposed to address the computational issues. However, it is difficult for researchers to obtain real datasets from insurance companies to test metamodeling techniques and publish the results in academic journals. In this paper, we create synthetic datasets that can be used for the purpose of addressing the computational issues associated with the nested stochastic valuation of large variable annuity portfolios. The runtime used to create these synthetic datasets would be about 3 years if a single CPU were used. These datasets are readily available to researchers and practitioners so that they can focus on testing metamodeling techniques.

Automated software bots infiltrate online surveys and corrupt data integrity, not to mention waste researcher time and budgets. Although resources exist to help keep bots out and identify bots when they do evade survey barriers, bot attacks may be a persistent problem for online surveys for a long time to come. Bots are evolving -- even as survey designers try ever more sophisticated methods to fend them off and weed their answers out. Vigilance needs to be high and the bot generators should not be under-estimated. We recount here some bot features we encountered after our own survey was attacked that helped to identify them, and that have not been detailed elsewhere. We also discuss reasons why commonly recommended strategies for how to keep bots out may not be feasible for many scientific researchers.

This paper is devoted to change-point detection using only the ordinal structure of a time series. A statistic based on the conditional entropy of ordinal patterns characterizing the local up and down in a time series is introduced and investigated. The statistic requires only minimal a priori information on given data and shows good performance in numerical experiments.

In this paper a robust version of the Wald test statistic for composite likelihood is considered by using the composite minimum density power divergence estimator instead of the composite maximum likelihood estimator. This new family of test statistics will be called Wald-type test statistics. The problem of testing a simple and a composite null hypothesis is considered and the robustness is studied on the basis of a simulation study. Previously, the composite minimum density power divergence estimator is introduced and its asymptotic properties are studied.

Pulsed-field gradient (PFG) diffusion experiments can be used to measure anomalous diffusion in many polymer or biological systems. However, it is still complicated to analyze PFG anomalous diffusion, particularly the finite gradient pulse width (FGPW) effect. In practical applications, the FGPW effect may not be neglected such as in clinical diffusion magnetic resonance imaging (MRI). Here, two significantly different methods are proposed to analyze PFG anomalous diffusion: the effective phase shift diffusion equation (EPSDE) method and an observing the signal intensity at the origin method. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space. However, these two approaches give the same general PFG signal attenuation including FGPW effect, which can be numerically evaluated by a direct integration method. The direct integration method is fast and without overflow. It is a convenient numerical evaluation method for Mittag-Leffler function type PFG signal attenuation. The methods here provide a clear view of spin evolution under field gradient, and their results will help the analysis of PFG anomalous diffusion.

The main goal of this article is to demonstrate the impact of environmental data on the spreading of Covid-19. In this research, data has been collected from 70 cities/provinces that are affected by Covid-19. Here, environmental data refers to temperatures, humidity and population density in each of these cities/provinces. This data has been analyzed using statistical models such as Poisson, Quasi-Poisson and negative Binomial. It is found that a negative Binomial regression model is the best fit for our data. Our results reveal that average high temperature is the vital factor to slow down the spread of Covid-19. In addition, higher population density found to be an important factor for the quick spreading of Covid-19 where it is quite impossible to maintain the social distance and the virus can spread easily.

This paper aims to describe the geometrical structure and explicit expressions of family of finitely parametrized probability densities over smooth manifold $M$. The geometry of family of probability densities on $M$ are inherited from probability densities on Euclidean spaces $\left\{U_\alpha \right\}$ via bundle morphisms, induced by an orientation-preserving diffeomorphisms $\rho_\alpha:U_\alpha \rightarrow M$. Current literature inherits densities on $M$ from tangent spaces via Riemannian exponential map $\exp: T_x M \rightarrow M$; densities on $M$ are defined locally on region where the exponential map is a diffeomorphism. We generalize this approach with an arbitrary orientation-preserving bundle morphism; we show that the dualistic geometry of family of densities on $U_\alpha$ can be inherited to family of densities on $M$. Furthermore, we provide explicit expressions for parametrized probability densities on $\rho_\alpha(U_\alpha) \subset M$. Finally, using the component densities on $\rho_\alpha(U_\alpha)$, we construct parametrized mixture densities on totally bounded subsets of $M$. We provide a description of inherited mixture product dualistic geometry of the family of mixture densities.

While the COVID-19 outbreak was reported to first originate from Wuhan, China, it has been declared as a Public Health Emergency of International Concern (PHEIC) on 30 January 2020 by WHO, and it has spread to over 180 countries by the time of this paper was being composed. As the disease spreads around the globe, it has evolved into a worldwide pandemic, endangering the state of global public health and becoming a serious threat to the global community. To combat and prevent the spread of the disease, all individuals should be well-informed of the rapidly changing state of COVID-19. In the endeavor of accomplishing this objective, a COVID-19 real-time analytical tracker has been built to provide the latest status of the disease and relevant analytical insights. The real-time tracker is designed to cater to the general audience without advanced statistical aptitude. It aims to communicate insights through various straightforward and concise data visualizations that are supported by sound statistical foundations and reliable data sources. This paper aims to discuss the major methodologies which are utilized to generate the insights displayed on the real-time tracker, which include real-time data retrieval, normalization techniques, ARIMA time-series forecasting, and logistic regression models. In addition to introducing the details and motivations of the utilized methodologies, the paper additionally features some key discoveries that have been derived in regard to COVID-19 using the methodologies.

The present reality about the Nigerian economy calls for investment and development in the non-oil sector. This becomes necessary as a result of fall in the oil price in the global market. This paper examined the Bayesian Vector Autoregression (BVAR) modeling and forecasting of the dynamic interrelationship between Economic growth and revenue from the oil and non-oil sectors in Nigeria. To achieve this, annual data on Gross Domestic Product (GDP), revenue from oil and non-oil sectors were collected from Central Bank of Nigeria (CBN) bulletin, the sample from 1981 to 2008 was used for analysis, while sample from 2009 to 2014 was used for model validation. Six (6) versions of Sims-Zha BVAR models were compared for out-of-sample forecast, the result revealed the superiority of the BVAR6 model over the other BVAR models. Lastly, evidence from the decomposition forecast errors revealed that revenue of oil sector contributed 7.69% to GDP while revenue from non-oil sector contributed 0.12% to GDP in Nigeria. This paper therefore recommended that the present government should encourage investment that is geared toward development in the non-oil sector, of which it has the capacity to improve the Economic growth of the Nigerian economy.

This paper has two major parts. In the first part histogram equalization for the image enhancement was implemented without using the built-in function in MATLAB. Here, at first, a color image of a rat was chosen and the image was transformed into a grayscale image. After this conversion, histogram equalization was implemented on the grayscale image. Later on, in the same image for each RGB channel, histogram equalization was implemented to observe the effect of histogram equalization on each channel. In the end, the histogram equalization was implemented to this specific color image of a rat. In the second part, for the grayscale image in part 1, the desired histogram of another colored image of a rat was introduced and histogram specification was implemented on the original colored image.

Many scientific and technological problems are studied with the help of computer codes that simulate the phenomena of interest rather than via traditional laboratory experiments. Such models play an important role in neuroscience where they are used to mimic brain function from the sub-cellular to the macroscopic level. Exploration with computer models carries with it a number of statistical challenges: where to sample the input space for the simulator, how to make sense of the data that is generated, how to estimate unknown parameters in the model, how to validate a model. The simulator setting also has some unique problems and possibilities. This review paper describes statistical research on these issues and how that work might be applied to neural simulations.

We propose a novel credit risk measurement model for Corporate Default Swap spreads, that combines vector autoregressive regression with correlation networks. We focus on the sovereign CDS spreads of a collection of countries, that can be regarded as idiosyncratic measures of credit risk. We model them by means of a vector autoregressive regression model, composed by a time dependent country specific component, and by a contemporaneous component that describes contagion effects among countries. To disentangle the two components, we employ correlation networks, derived from the correlation matrix between the reduced form residuals. The proposed model is applied to ten countries that are representative of the recent financial crisis: top borrowing/lending countries, and peripheral European countries. The empirical findings show that the proposed model is a good predictor of CDS spreads movements, and that the contemporaneous component decreases prediction errors with respect to a simpler autoregressive model. From an applied viewpoint, core countries appear to import risk, as contagion increases their CDS spread, whereas peripheral countries appear as exporters of risk. Greece is an unfortunate exception, as its spreads seem to increase for both idiosyncratic factors and contagion effects.

A vast majority of the countries is under the economic and health crises due to the current epidemic of coronavirus disease 2019 (COVID-19). The present study analyzes the COVID-19 using time series, which is an essential gizmo for knowing the enlargement of infection and its changing behavior, especially the trending model. We have considered an autoregressive model with a non-linear time trend component that approximately converted into the linear trend using the spline function. The spline function split the COVID-19 series into different piecewise segments between respective knots and fitted the linear time trend. First, we obtain the number of knots with its locations in the COVID-19 series and then the estimation of the best-fitted model parameters are determined under Bayesian setup. The results advocate that the proposed model/methodology is a useful procedure to convert the non-linear time trend into a linear pattern of newly coronavirus case for various countries in the pandemic situation of COVID-19.

The goal of VAR or BVAR is the characterization of the dynamics and endogenous relationships among time series. Also the VAR models are known for their applications to forecasting and policy analysis. This paper compare the performance of VAR and Sims-Zha Bayesian VAR models when the multiple time series are jointly influenced by different levels of collinearity and autocorrelation in the short term (T=16, 32, 64 and 128). Five levels (-0.9,-0.5, 0,+0.5,+0.9) of collinearity and autocorrelation were considered and the results from the simulation study revealed that VAR(2) model dominated for no and moderate levels of autocorrelation (-0.5, 0, +0.5) irrespective of the collinearity level except in few cases when T=16. While the BVAR models dominated for high autocorrelation levels (-0.9 and +0.9) irrespective of the collinearity level except in few cases when T=128. The performance of the models varies at different levels of the collinearity and autocorrelated error, and also varies with the short term periods. Furthermore, the values of the RMSE and MAE criteria decrease as a result of increase in the time series length. In conclusion, the performance of the forecasting models depend on the time series data structure and the time series length. It is therefore recommended that the data structure and series length should be considered in using an appropriate model for forecasting.

Developments of new probability models for data analysis are keen interest of importance for all fields. The log-Dagum distribution has a prominent role in the theory and practice of statistics. In this article, a new family of continuous distributions generated from a log Dagum random variable called the log-Dagum Weibull distribution is proposed. The key properties of the proposed distribution are derived. Its density function can be symmetrical, left-skewed, right-skewed and reversed-J shaped and can have increasing, decreasing, bathtub hazard rates shaped. The model parameters are estimated by the method of maximum likelihood and illustrate its importance by means of applications to real data sets.

In financial time series modelling and forecasting, combining ARMA and GARCH models tend to produce superior and reliable models for volatility persistence, half-life volatility and backtesting (application of model in real life). In Nigeria, banking stocks are mostly traded because of its potential benefits to investors. This study modelled and forecasted the Guaranty Trust (GT) Bank daily stock returns from January 2^nd 2001 to May 8^th 2017 data set collected from a secondary source. The ARMA-GARCH models, persistence, half-life and backtesting were used to analysed the collected data using student t and skewed student t distributions, and the analyses are carried out R environment using rugard and performanceAnaytics Packages. The study revealed that using the lowest information criteria values only could be misleading rather we added the use of backtesing. The ARMA(1,1)-GARCH(1,1) models fitted exhibited high persistency in the daily stock returns while the days it takes for mean-reverting of the models ranges from 5 days to 100 days but unfortunately the models failed backtesting. The results further revealed ARMA(1,1)-eGARCH (2,2) model with student t distribution provides a suitable model for evaluating the GT bank stock returns among the competing models while it takes less than 30 days for the persistence volatility to return back to its average value of the stock returns. This study recommended that researchers should adopt backtesting approach while fitting GARCH models while GT bank stocks investor should be assured that no matter the fluctuations in the stock market, the GT bank stock returns has the ability to returns to its mean price return.

We derive a concentration inequality for the uncertainty in the mean computed by stratified random sampling, and provide an online sampling method based on this inequality. Our concentration inequality is versatile and considers a range of factors including: the data ranges, weights, sizes of the strata, the number of samples taken, the estimated sample variances, and whether strata are sampled with or without replacement. Sequentially choosing samples to minimize this inequality leads to a online method for choosing samples from a stratified population. We evaluate and compare the effectiveness of our method against others for synthetic data sets, and also in approximating the Shapley value of cooperative games. Results show that our method is competitive with the performance of Neyman sampling with perfect variance information, even without having prior information on strata variances. We also provide a multidimensional extension of our inequality and discuss future applications.

All transmission disease depends on the transmission opportunity or medium like humans in COVID-19. Due to globalization and regular movement of people from one country to another, spread of COVID 19 reached to 208 countries till May 10, 2020. For any society health is major concern for humanity as well as administration. Any pandemic is declared as and when it reached at a particular severity level and control vice versa. So, we have continued the daily COVID 19 cases analysis and segregated till May 10, 2020. We have included at least 25 countries for the analysis purpose due to limitation of number of observations in the analysis. Maximum number of day’s data available for China is for 100 days, followed by Iran for 81 days, minimum number of days data is for 16 days for Western Sahara and Tajikistan.

Most existing flexible count regression models allow only approximate inference. This work proposes a new framework to provide an exact and flexible alternative for modeling and simulating count data with various types of dispersion (equi-, under- and overdispersion). The new method, referred as “balanced discretization”, consists in discretizing continuous probability distributions while preserving expectations. It is easy to generate pseudo random variates from the resulting balanced discrete distribution since it has a simple stochastic representation in terms of the continuous distribution. For illustrative purposes, we have developed the family of balanced discrete gamma distributions which can model equi-, under- and overdispersed count data. This family of count distributions is appropriate for building flexible count regressionmodels because the expectation of the distribution has a simple expression in terms of the parameters of the distribution. Using the Jensen–Shannon divergence measure, we have shown that under equidispersion restriction, the family of balanced discrete gamma distributions is similar to the Poisson distribution. Based on this, we conjecture that while covering all types of dispersion, a count regression model based on the balanced discrete gamma distribution will allow recovering a near Poisson distribution model fit when the data is Poisson distributed.

This paper has three objectives, the first is to present a detailed overview in the form of a tutorial for the developments of several key quantile time series modelling approaches. The second objective is to develop a general framework to represent such quantile models in a unifying manner in order to easily develop extensions and connections between existing models that can then be developed to further extend these models in practice. In this regard, the core theme of the paper is to provide perspectives to a general audience of core components that go into construction of a quantile time series model and then to explore each of these core components in detail. The paper is not addressing the concerns of estimation of these models, as there is existing literature on these aspects in many settings, we provide references to relevant works on these aspects in several classes of model. Instead, the focus is rather to provide a unified framework to construct such models for practitioners, therefore the focus is instead on the properties of the models and links between such models from a constructive perspective. The third objective is to compare and discuss the application of the different quantile time series models on several sets of interesting demographic and mortality based time series data sets of relevance to life insurance analysis. The exploration included detailed mortality, fertility, births and morbidity data in several countries with more detailed analysis of regional data in England, Wales and Scotland.

The statistical bundle is the set of couples $(Q,W)$ of a probability density Q and a random variable W such that $\mathbb{E}$_Q [W] = 0. On a finite state space, we assume Q to be a probability density with respect to the uniform probability and give an affine atlas of charts such that the resulting manifold is a model for Information Geometry. Velocity and accelleration of a one-dimensional statistical model are computed in this set up. The Euler-Lagrange equations are derived from the Lagrange action integral. An example of Lagrangian using minus the entropy as potential energy is briefly discussed.

Dispersion tests based on the second order component of smooth test statistics are related to Fisher’s Index of Dispersion test, used for testing for the Poisson distribution when there are no covariates present. Such tests have been recommended in [1] to test for the Poisson distribution when covariates are present. The modified Borel-Tanner (MBT) distribution seems suited to data with extra zeroes, a monotonic decline in counts and longer tails. Here we recommend a dispersion test for the MBT distribution for both when covariates are absent and when they are present.

Tuberculosis cause of death worldwide and the leading cause from a single infectious agent, ranking above Human immunodeficiency virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS). The aim of this study is to ascertain the trend of tuberculosis prevalence and the effect of HIV prevalence onl Tuberculosis case in some West African countries from 2000 to 2016 using count panel data regression models. The data used annual HIV and Tuberculosis cases spanning from 2000 to 2016 extracted from online publication of World health Organization (WHO). Panel Poisson regression model and Negative binomial regression model for fixed and random effects were used to analyzed the count data, the result revealed a positive trend in TB cases while increased in HIV cases leads to increase in TB cases in West African countries. Among the competing models used in this study, Panel Negative Binomial Regression Model with fixed effect emerged the best model with log likelihood value of -1336.554. This study recommended that Government and NGOs need more strategies to fight against HIV menace in West Africa as this will in turn reduced TB cases in West Africa.

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densi- ties and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on dierent set of true values. Some real data sets were employed to show the usefulness and exibility of the model which serves as generalization to many sub-models in the elds of engineering, medical, survival and reliability analysis.

The hourly and daily rainfall data which is spatially distributed are required as an input for run-off rain model. Furthermore, the run-off rain model is used to detect early flooding. The daily and hourly rainfall data have characteristics that most of data are zero. Therefore we need a model which can capture the phenomenon. A time series model involving location, which is a model that can be developed to approach the daily and hourly rainfall data, we can call Vector Autoregressive (VAR) model. The VAR model allows us for modeling rainfall data in several areas. However, in certain conditions the VAR model often occurs over-parameterization and reduces degrees of freedom. The aim of this study is to compare the VAR model with Maximum Likelihood Estimator (MLE) and Bayesian to hourly and daily rainfall data in SampeanWatershed of Bondowoso. The results showed that the hourly and daily rainfall data are fitted to VAR process of orde 5 and 1 respectively. Based on the AIC and SBC values indicate that the Bayesian is better than the MLE method. The Bayesian is able to predict parameters by producing a smaller variance covariance matrix than the MLE.

Location-and-scale transformation of a random variable underpins normal distribution, but it is however fundamentally incorrect for scale estimation such as relative dispersion. In this paper, a parametrized alternative to a normal distribution, called scaloc-normal distribution, is proposed that efficiently works and is fundamentally correct with absolute and relative dispersion estimators. The Monte Carlos simulation experiment was used to generate a total of 600,000 artificial datasets in 600 different simulation scenarios from loc-normal (normal) and scaloc-normal distributions. The absolute and relative dispersion were estimated and compared from the two distributions. The results show that scaloc-normal distribution is a good parametrized alternative to loc-normal distribution, fundamentally correct and efficient with both standard deviation and coefficient of variation. The key statistical advancement from loc-normal to scaloc-normal distribution is its fundamental correctness (i.e., scale-invariant property) with an efficient relative estimator of dispersion (i.e., coefficient of variation). Parametrically, the loc-normal and scaloc-normal distributions are very different, but both have linear transformations.

In most econometrics literature, the Autoregressive Distributed Lag (ARDL) model is often applied in many economic analyses to study short and long run relationships. This is because ARDL model can deal with economic variables that are integrated of different order (I(0), I(1) or combination of both) and also it is robust where there is single long-run relationship between the underlying variables in a simple sample size. This study applied the ARDL model to examine the contributions of commercial Banks to GDP growth in Nigeria. To achieve this, annual data covering 1981 to 2015 for loans and advances, savings, lending rates and GDP of Financial Institutions were collected from CBN bulletin. The ADF test revealed that the variables are I(1) except for lending rate which was of I(0) order. The ARDL(1,1,1,2) model revealed that loans and advances, and lending rates are significantly positively related to GDP in Nigeria but savings was not significant in the model. The model revealed some evidence of short run relationships while the ecm(-1) was -0.6156 (P-value=0.0038<0.05) which means that the rate of the speed of adjustment to equilibrium is 61.56% annually. The estimated model is free from serial correlation, multicollinearity, heteroscedasticity while the model is stable and the residuals are normally distributed. The study recommends that savings and savings culture should be encouraged in Nigeria since economic theory states that savings and investment are related in any economic development.

The research work examined the trend of HIV/AIDS, Tuberculosis, and Hepatitis diseases in Plateau state. Annual data from 2003 to 2018 was collected from the department of biostatistics at Plateau State Specialist Hospital (PSSH), Jos. The methods of analysis used are the Poisson Autoregressive Model (PAR(1)) and the Poisson Exponentially Weighted Moving Average Model (PEWMA). The results revealed a significant annual decrease of 23.9% and 4% in Tuberculosis and HIV/AIDS respectively. Furthermore, the results showed a significant annual increase of 46% in Hepatitis. The PEWMA model used revealed that TB increased by 0.02% when there is an increase in HIV but not significant, while Hepatitis significantly aggravates TB by at least 0.24%. Also, there is a significant rise in HIV by 0.85% when TB increases but Hepatitis has no such effect on HIV. Lastly, PEWMA model indicated a rise of 0.5% in Hepatitis cases when there is an increase in TB, but a surge in HIV has no such effect on Hepatitis cases in Jos. The study recommended that fight against TB should be intensified since TB cases significantly affect both HIV and Hepatitis in Jos, Nigeria.

In this research first, a sequence of properties called delta is assigned to each prime number and then examined. Deltas are only dependent on the distribution of prime numbers, so the results obtained for the delta distribution can be considered as a proxy for the distribution of prime numbers. The first observation was that these properties are not unique and different prime numbers may have the same value of delta of a given order. It was found that a small number of deltas cover a large portion of prime numbers, so by recognizing repetitive deltas, the next prime numbers can be predicted with a certain probability, but the most important observation of this study is the normal distribution of deltas. This research has not tried to justify the obtained observations and instead of answering the questions, it seeks to ask the right question.

The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the comparison of the maximum likelihood estimates and the Bayes estimates of two-parameter power function distribution. The Bayes estimates are obtained, using conjugate priors, under five loss functions consist of square error, precautionary, weighted, LINEX and DeGroot loss function. The Gibbs sampling algorithm is proposed to generate samples from posterior distributions and in result the Bayes estimates are computed. The comparison of the maximum likelihood estimates and the Bayes estimates are done through the root mean squared errors. One real-life data set is analyzed to illustrate the evaluation of proposed methods of estimation. Finally, results from the simulation are discussed to assess the performance behavior of the maximum likelihood estimates and the Bayes estimates.

This study investigated the trends of registered Death and Birth in Nigeria using Generalized Linear Models. Annual data on Death and Birth was collected from National Population Commission for the period of 2004 to 2017. The Natural increase calculated revealed a positive trend in the natural increase in Nigeria from 2004 to 2017. Evidence from summary statistics revealed some level of over dispersion (variance > mean). This study explored Poisson Regression Models and Negative Binomial Regression Models using two links (identity and log). The results revealed a positive increase in registration of birth and death rates in Nigeria and among the competing the models, Negative Binomial regression model with identity link emerged as the best model for modeling birth and death rates registration in Nigeria. Data on numbers of deaths and causes of death are essential if countries are to determine priorities, formulate and monitor policies for public health care as well as other government policies that may be based on such data

Bayesian nonlinear mixed effects models for data in the form of continuous, repeated measurements from a population, also known as Bayesian hierarchical nonlinear models, are a popular platform for analysis when interest focuses on individual specific characteristics and relevant uncertainty quantification. Due to the limitation of computational power, this framework was relatively dormant until the late 1980s, but in recent years, the statistical research community saw vigorous development of new methodological and computational techniques for these models, the emergence of software, and wide application of the models in numerous industrial and academic fields. This article presents an overview of the formulation, interpretation, and implementation of Bayesian nonlinear mixed effects models and surveys recent advances and applications.

For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions from a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de-Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for estimating the family parameters. We investigate the properties of one special model called a new Kumaraswamy-Weibull (NKwW) distribution. Parameter estimation is dealt and maximum likelihood estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of this distribution. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-Weibull, McDonald-Weibull, beta-Weibull, exponentiated-generalized Weibull, gamma-Weibull, odd log-logistic-Weibull, Marshall-Olkin-Weibull, transmuted-Weibull, exponentiated-Weibull and Weibull distributions when applied to these data sets. The bivariate extension of the family is proposed and the estimation of parameters is given. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set.

The crux of the paper is to present a detailed analysis of COVID-19 data which is available on global basis. This analysis is performed using some specific package of R software. It provides various insights from the data and help to understand the current status of this pandemic in India so that effective measures can be formulated by policymakers. These insights include global summary of this disease, growth rate of this pandemic and performance of SIR model for the given global data. The analysis has been presented in different tables and graphs to understand the outputs of the problem in a more detailed point of view.

Total Nigeria Plc is a Marketing and Services subsidiary of Total; a multinational energy company operating in more than 130 countries and committed to providing sustainable products and services for its customers. For over 50 years, Total Nigeria Plc has remained the leader in the downstream sector of the Nigerian oil and gas industry. This study investigated the volatility of the stock price of Total Petroleum Nigeria plc using nine (9) GARCH models namely sGARCH, gjrGARCH, eGARCH, iGARCH, aPARCH, TGARCH, NGARCH, NAGARCH and AVGARCH. We also investigated the Value-at-Risk (VaR) and Backtesting of the Models. The aim actually of this study is to boost the confidence of the shareholders and investors of the Total Nigeria plc. To achieve this, daily stock price for Total petroleum Nigeria plc from secondary was collected from January 2^nd 2001 to May 8^th 2017. . The study used both normal and student t innovations, using Akaike Information Criterion (AIC) to select the best model, for normal innovations for log returns and cleansed log returns of Total plc, the eGARCH and sGARCH models performed best respectively, while NGARCH model performed best for student t innovation for both log returns and cleansed returns of Total plc. The persistence of the models are stable except in few cases where iGARCH, eGARCH where not stable. Also for student t innovation, the sGARCH and gjrGARCH fails to converge. The mean-reverting number of day for the returns of Total Nigeria plc differs from model to model. Evidence from the VaR Analysis revealed from the selected models revealed that the Risk of VaR losses is high at 99% confidence level, slightly high at 95% confidence level and better at 90% confidence level. Although The Duration-Based Tests of independence conducted revealed that the models are correctly specified since in all cases the null hypotheses were accepted. This means that the probability of an exception on any day did not depends on the outcome of the previous day. Finally, both the unconditional (Kupiec) and conditional (Christoffersen) coverage tests for the correct number of exceedances for both Total stock returns and cleansed returns. The tests revealed rejection of the models at 1% level of significance. This confirms that unconditional (Kupiec) and conditional (Christoffersen) coverage tests for the correct number of exceedances are reliable compared to the Duration-Based Tests of independence. Therefore we recommend that shareholders and investors in Total Nigeria plc are to remain and continue to investment in Total Nigeria plc because if there is any form of losses, the price of the stock has the potentials to improve in the future. Again, though the risk is high at 99% confidence level, this in line with the financial theory that states that an asset with high expected risk would pay higher return on the average.

Background: In the functional data analysis (FDA), the hybrid or mixed data are scalar and functional datasets. The semi-functional partial linear regression model (SFPLR) is one of the first semiparametric models for the scalar response with hybrid covariates. Various extensions of this model are explored and summarized. Methods: Two first research articles, including “semi-functional partial linear regression model”, and “Partial functional linear regression” have more than 300 citations in Google Scholar. Finally, only 106 articles remained according to the inclusion and exclusion criteria such as 1) including the published articles in the ISI journals and excluding 2) non-English and 3) preprints, slides, and conference papers. We use the PRISMA standard for systematic review. Results: The articles are categorized into the following main topics: estimation procedures, confidence regions, time series, and panel data, Bayesian, spatial, robust, testing, quantile regression, varying Coefficient Models, Variable Selection, Single-index model, Measurement error, Multiple Functions, Missing values, Rank Method and Others. There are different applications and datasets such as the Tecator dataset, air quality, electricity consumption, and Neuroimaging, among others. Conclusions: SFPLR is one of the most famous regression modeling methods for hybrid data that has a lot of extensions among other models.

Bootstrapping is a flexible, powerful and well-established statistical approach to quantify the uncertainty of virtually any point estimate. While multiple versions of bootstrap confidence intervals are already available in Stata, dbs implements the double (iterated) bootstrap. Instead of relying on parametric assumptions such as the non-parametric resampling bootstrap confidence interval does, it is more flexible and derives critical values directly from that data. To do so, multiple methods are available (analytic approach, double resampling, jackknife estimation). In a comparative simulation study it is empirically demonstrated that the strengths of the double bootstrap are particularly evident for small samples (n < 100) when heteroscedasticity is present. While all other approaches result in undercoverage, only the double bootstrap reaches the target coverage level and hence avoids incorrect statistical conclusions. The computational burden is not even necessarily larger than for other bootstrap approaches.

A variable annuity is a popular life insurance product that comes with financial guarantees. Using Monte Carlo simulation to value a large variable annuity portfolio is extremely time-consuming. Metamodeling approaches have been proposed in the literature to speed up the valuation process. In metamodeling, a metamodel is first fitted to a small number of variable annuity contracts and then used to predict the values of all other contracts. However, metamodels that have been investigated in the literature are sophisticated predictive models. In this paper, we investigate the use of linear regression models with interaction effects for the valuation of large variable annuity portfolios. Our numerical results show that linear regression models with interactions are able to produce accurate predictions and can be useful additions to the toolbox of metamodels that insurance companies can use to speed up the valuation of large VA portfolios.

The constant news about the corona virus is scary. It is not possible to separate treatment for Cancer due to COVID-19. An effective treatment comparison strategy is needed. We need to have a handy tool to understand cancer progression in this unprecedented scenario. Linking different events of cancer progression is the need of the hour. It is a methodological challenge. We provide the solutions to overcome the issue with interval between two consecutive events in motivating head and neck cancer (HNC) data.

In this paper we describe a nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions. Given $N$ independent observations, convexity theory shows that the NPML estimator is discrete with at most $N$ support points. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. The probability of the support points is found by a Primal-Dual Interior-Point method; the location of the support points is found by an Adaptive Grid method. Our method is able to handle high-dimensional and complex multivariate mixture models.An important application is discussed for the problem of population pharmacokinetics and a non-trivial example is treated.Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics.

Validation and verification are the critical requirements in the knowledge acquisition method for the clinical decision support system (CDSS). After acquiring the medical knowledge from diverse sources, the rigorous validation and formal verification process are required before creating the final knowledge model. Previously, we have proposed a hybrid knowledge acquisition method for acquiring medical knowledge from clinical practice guidelines (CPGs) and patient data in the Smart CDSS for treatment of oral cavity cancer. The final knowledge model was created by combining knowledge models obtained from CPGs and patient data after passing through a rigorous validation process. However, detailed analysis shows that due to lack of formal verification process, it involves various inconsistencies in knowledge relevant to the formalism of knowledge, conformance to CPGs, quality of knowledge, and complexities of knowledge acquisition artifacts. Therefore, it is required to enhance a hybrid knowledge acquisition method that thwarts the inconsistencies using formal verification. This paper presents the verification process using the Z formal method and its outcome as an enhanced acquisition method – known as the refined knowledge acquisition (ReKA) method. The ReKA method adopted verification method and explored the mechanism of theorem proving using the Z notation. It enables to identify inconsistencies in the validation process used for hybrid knowledge acquisition. Additionally, it refines the hybrid knowledge acquisition method by discovering the missing steps in the current validation process at the acquisition stage. Consequently, ReKA adds a set of nine additional criteria to be used to have a final valid refined clinical knowledge model. The criteria ensure the validity of final knowledge model concerning formalism of knowledge, conformance to GPGs, quality of the knowledge, usage of stringent conditions and treatment plans, and inconsistencies possibly resulting from the complexities. Evaluation, using four medical knowledge acquisition scenarios, shows that newly added knowledge in CDSS due to the addition of criteria by ReKA method always produces a valid knowledge model. The final knowledge model was also evaluated with 1229 oral cavity patient cases, which outperformed with an accuracy of 72.57\% compared to a similar approach with an accuracy of 69.7\%. Furthermore, ReKA method identified a set of decision paths (about 47.8%) in the existing approach, which results in a final knowledge model with low quality, non-conformed from standard CPGs. In conclusion, ReKA is formally proved method which always yields valid knowledge model having high quality, supporting local practices, and influenced from standard guidelines.

The central limit theorem (CLT) and its generalization to stable distributions have been widely described in literature. However, many variations of the theorem have been defined and often their applicability in practical situations is not straightforward. In particular, the applicability of the CLT is essential for a derivation of heterogeneous ensemble of Brownian particles (HEBP). Here, we analyze the role of the CLT within the HEBP approach in more detail and derive the conditions under which the existing theorems are valid.

This paper considers estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the Log--Huber loss function which is resistant to outliers and useful to find robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of Bayesian risk function with themselves as well as the usual plug-in density ratio estimators. Some applications such as classification and divergence function estimation are addressed.

Malaria is endemic in Nigeria and remains a major public health problem, taking its greatest toll on children under age 5 and pregnant women, although it is preventable, treatable, and curable. This study investigates the Impact of socio-economic factors and indoor mosquito control on malaria prevalent among pregnant women in Nigeria using logistic regression. To achieve this, secondary data obtained from 2015 Nigeria Malaria Indicator survey, executed by the National Malaria Elimination Programme (NMEP) and the National Population Commission (NPopC), with a nationally representative sample of more than 8,000 consisting of 7,745 households. The results from the logistic regression with odds ratio revealed that pregnant women are more like to be affected by malaria fever (though not significant) compared to women that are not pregnant. The income levels of the household does not significant reduce the incidence of malaria fever among pregnant women in Niger. Concerning the malaria presenting measure, only dwelling sprayed by private company significantly reduce the incidence of malaria fever among pregnant women (P-value=0.020<0.05) compared to dwelling sprayed by government and NGOs and also to Insecticide Treated Net. Also pregnant women in the urban centers are less likely to have malaria fever compared to pregnant women in rural communities in Nigeria. Also, pregnant women with atleast a secondary school level of education are less likely to be affected by malaria fever compared to pregnant women with no formal education. The fitted logistic model passed the goodness-of-test fit; the classification test for the logistic model was correctly classified at about 67.02%. Therefore, this study recommends that government and NGOs should intensify their efforts in the area of dwelling spraying, awareness campaign of the danger of malaria fever among pregnant women and infants, engaged in effective distribution of insecticide treated net in order to reduce the incidence of malaria fever among pregnant women living in rural communities in Nigeria.

This study explores students’ understanding of one measure of central tendency, the mean. A teaching experiment was conducted to understand how sixth-grade students made sense of this concept. Findings suggest that the students know how to solve mathematical problems related to mean using procedural understanding and lack of conceptual understanding.

Analyzing big data poses a great challenge for numerous researchers to explore the data structure. Dimension reduction methods can be used to reduce data dimensionality, taking it from occupying a high-dimensional space to existing in a lower-dimensional space while retaining as much information as possible. Principal Component Analysis is one of the most popular used to reduce the dimensional space. The bootstrap sample is obtained by randomly sampling n times with replacement from the original sample, the method provides easy tool to understand the interactive component and develop the process. There are not enough researches discussed the stability of PCA method using bootstrap method. In this paper, the bootstrap method is used to analyze the stability of PCA results and to estimate the number of PCA in efficient way. The method is used to estimate the number of PCA that needed to classify the data set, and the effectiveness of the discussed techniques is demonstrated through real data sets.

Interpolation is procedure that depends on spatial and/or statistical properties of analysed variable(s). It is special challenging task for data that included low number of samples, like dataset with less than 20 data. This problem is especially emphasized in the subsurface geological mapping, i.e. in the cases where data are taken solely from wells. Successful solutions of such mapping problems ask for knowledge about interpolation methods designed primarily for small datasets and dataset itself. Here are compared two methods, namely Inverse Distance Weighting and Modified Shepard’s Method, applied for three variables (porosity, permeability, thickness) measured in the Neogene sandstone hydrocarbon reservoirs (Northern Croatia). The results showed that pure cross-validation is not enough condition for appropriate map selection, but also geometrical features need to be considered, for datasets with less than 20 points.

We show how some concentration inequalities for sampling without replacement can be used for bounding future samples. This process can be extended to bound the sum of future samples from multiple populations, and we analyse an illustrative sample allocation problem.

This paper addresses the issues of how we can quantify structural information for nonparametric distributions and how we can detect its changes. Structural information refers to an index for a global understanding of a data distribution. When we consider the problem of clustering using a parametric model such as a Gaussian mixture model, the number of mixture components (clusters) can be thought of as structural information in the model. However, there does not exist any notion of structural information for nonparametric modeling of data. In this paper we introduce a novel notion of {\em kernel complexity} (KC) as structural information in the nonparametric setting. The key idea of KC is to combine the information bias inspired by the Gini index with the information quantity measured in terms of the normalized maximum likelihood (NML) code length. We empirically show that KC has a property similar to the number of clusters in a parametric model. We further propose a framework for structural change detection with KC in nonparametric distributions. With synthetic and real data sets we empirically demonstrate that our framework enables us to detect structural changes underlying the data and their early warning signals.

Since its post-World War II inception, the science of record linkage has grown exponentially and is used across industrial, governmental, and academic agencies. The academic fields that rely on record linkage are diverse, ranging from history to public health to demography. In this paper, we introduce the different types of data linkage and give a historical context to their development. We then introduce the three types of underlying models for probabilistic record linkage: Fellegi-Sunter based methods, machine learning methods, and Bayesian methods. Practical considerations such as data standardization and privacy concerns are then discussed. Finally, recommendations are given for organizations developing or maintaining record linkage programs, with an emphasis on organizations measuring long-term complications of disasters such as 9/11.

The paper is concerned with a class of stochastic differential equations in infinite dimensional Hilbert space with random coefficients driven by Teugel's martingales which are more general processes. and its optimal control problem. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with L\'{e}vy processes (see Nualart and Schoutens). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classicconvex variation method and dual technique.The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.

The road traffic injuries risk factors such as driving offenses and average speed are concerns for health organizations to reduce the number of injuries. Without any comprehensive view of each road, one cannot decide about the effective policy. In this manner, the data-driven policy will help to improve and assess the decisions. The count data near the road of two airports is surveyed for investigating the time-varying speed zones. The descriptive statistics, ANOVA, and functional data analysis were used. The hourly data of traffic counts for four different locations at the entrance of the two airports, international and domestics, were collected for one the year 2018 to 2019.The hourly pattern of driving offenses for each road was assessed and the to and from airport roads had different peaks (<0.05). The hour, weekdays, type of airport, direction and their interactions were statistically significant (<0.05) for the chance of driving offenses. The speed average during the day was statistically different (<0.5) by the number of different types of vehicles. The traffic count data is a great resource for decision making in safe driving subjects such as driving offenses. With functional data analysis, we can analyze them to get the most of the characteristics of this data. The airports are public places with high traffic demand in all countries that yields the different pattern of traffic transportation, therefore we extract the factors that affect the driving offenses. Finally, we conclude that conducting a time-varying speed zone near the airports seems vital.

Study objective Since December 2019, the coronavirus disease (COVID-19) pandemic has caused over a million deaths and resulted in adverse socio-economic impacts worldwide. However, predictability and prognostication of clinical features vary among different populations. Methods We search PubMed, EMBASE, Cochrane Library, Google Scholar, and WHO Global Health Library from December 2019 to April 2020 for studies reporting the risk factors, clinical features, and outcomes. The random-effect models for transformed prevalence (single-arm) or bivariate random-effect models (sensitivity and specificity) for correlated performance indicators. Results Among the 189 included studies representing 53,659 patients, the most sensitive predictor for COVID-19 infection was fever in adults (83%, 95% confidence interval [CI]:73–90%), and the most specific predictor was fatigue (96%, 95% CI: 80–99%). Fever was the most sensitive symptom in predicting the severity (89%, 95% CI:83–92%), followed by cough (71%, 95% CI:63–78%). The most specific predictor of severe COVID-19 was a chronic obstructive pulmonary disease (99%, 95% CI:98–99%). The stage of the outbreak and age significantly affect the prevalence of fever, fatigue, cough, and dyspnea. Fever, cough, fatigue, hypertension, and diabetes mellitus combined have a 3.06 positive likelihood ratio (PLR) and a 0.59 negative likelihood ratio (NLR) in the diagnosis. Additionally, fever, cough, sputum production, myalgia, fatigue, and dyspnea combined have a 10.44 PLR and a 0.16 NLR in predicting severe COVID-19. Conclusions Understanding the different distribution of predictors essential for screening potential COVID-19 infection and severe outcomes and the combination of symptoms could improve the pre-test probability.

Circular RNAs are a special type of RNAs which recently attracted a lot of research interest in studying its formation and function. RNA binding proteins (RBPs) that bind circRNAs are important in these processes but are relatively less studied. CLIP-Seq technology has been invented and applied to profile RBP-RNA interactions on the genome-wide scale. While mRNAs are usually the focus of CLIP-Seq experiments, RBP-circRNA interactions could also be identified through specialized analysis of CLIP-Seq datasets. However, many technical difficulties are involved in this process, such as the usually short read length of CLIP-Seq reads. In this study, we created a pipeline called Clirc specialized for profiling circRNAs in CLIP-Seq data and analyzing the characteristics of RBP- circRNAs interactions. In conclusion, this is one of the first few studies to investigate circRNAs and their binding partners through repurposing CLIP-Seq datasets to our knowledge, and we hope our work will become a valuable resource for future studies into the biogenesis and function of circRNAs. Clirc software is available at https://github.com/Minzhe/Clirc

A paradigm shift away from null hypothesis significance testing seems in progress. Based on simulations, we illustrate some of the underlying motivations. First, P-values vary strongly from study to study, hence dichotomous inference using significance thresholds is usually unjustified. Second, statistically significant results have overestimated effect sizes, a bias declining with increasing statistical power. Third, statistically non-significant results have underestimated effect sizes, and this bias gets stronger with higher statistical power. Fourth, the tested statistical hypotheses usually lack biological justification and are often uninformative. Despite these problems, a screen of 48 papers from the 2020 volume of the Journal of Evolutionary Biology exemplifies that significance testing is still used almost universally in evolutionary biology. All screened studies tested default null hypotheses of zero effect with the default significance threshold of p = 0.05, none presented a pre-specified alternative hypothesis, pre-study power calculation, and the probability of ‘false negatives’(beta error). The results sections of the papers presented 49 significance tests on average (median 23, range 0–390). Of 41 studies that contained verbal descriptions of a ‘statistically non-significant’ result, 26 (63%) falsely claimed the absence of an effect. We conclude that studies in ecology and evolutionary biology are mostly exploratory and descriptive. We should thus shift from claiming to ‘test’ specific hypotheses statistically to describing and discussing many hypotheses (possible true effect sizes) that are most compatible with our data, given our statistical model. We already have the means for doing so, because we routinely present compatibility (‘confidence’) intervals covering these hypotheses.

This study has developed a Matlab application for simulating statistical models project (SMp) probabilistic distributions that are similar to binomial and Poisson, which were created by mathematical procedures. The simulated distributions are graphically compared with these legendary distributions. The application allows to obtain many probabilistic distributions, and shows the trend (τ ) for n trials with success probability p, i.e. the maximum probability as τ=np. While the Poisson distribution PD(x;µ) is a unique probabilistic distribution, where PD=0 in x=+∞, the application simulates many SMp(x;µ,Xmax) distributions, where µ is the Poisson parameter and value of x with generally the maximum probability, and Xmax is upper limit of x with SMp(x;µ,Xmax) ≥ 0 and limit of the stochastic region of the random discrete variable X. It is shown that by simulation via, one can get many and better probabilistic distributions than by mathematical one.