Healthcare leaders are faced with many financial challenges in the contemporary environment, leading to many bankruptcies in recent years. What is not well understood are the specific conditions that lead to organizational economic failure. Ideally, hospital leaders could examine the literature for guidance to predict bankruptcy before it occurs. However, existing regression methods have proven inadequate, especially when the finance variables follow a nonnormal frequency pattern. Furthermore, the regression approach encounters difficulties due to multicollinearity and nonnormality issues. Therefore, an alternate stochastic approach for predicting the probability of hospital bankruptcy is warranted. This new method includes computing and interpreting the correlations between the hospital’s revenue and expenses for bivariate lognormal data, calculating the risk of bankruptcy due to the mismatch between revenues and expenses, determining the likelihood of a hospital’s expense exceeding the state’s median expense level, and evaluating a hospital’s financial memory level. Ultimately in our research, we demonstrate a novel approach to anticipate hospital bankruptcy, which can be particularly useful for health policy analysts and hospital leaders in making informed financial decisions and proactively managing risks to ensure the sustainability and stability of their institutions.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

Germanium films were grown on c-plane sapphire with a 10 nm AlAs buffer layer using molecular beam epitaxy. The effects of Ge film thickness on the surface morphology and crystal structure were investigated by ex-situ characterization techniques. The nucleation of Ge proceeds by forming (111) oriented three-dimensional islands with two rotational twin domains about the growth axis. The boundaries between the twin grains are the origin of 0.2% strain and tilt grains. The transition to a single-grain orientation reduces the strain and results in a better-quality Ge buffer. Understanding the role of thickness on material quality during the Ge(111)/Al2O3(0001) epitaxy is vital for achieving device quality when using group IV material on the sapphire platform.

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.

In this paper we consider type II bivariate generalized power series Poisson distribution as a compound Poisson distribution with bivariate generalized power series compounding distribution. We obtain some properties, p.m.f. and conditional distributions. In addition we also give a brief discussion about the multivariate extension of this case. Then we introduce type II bivariate generalized power series Poisson process and consider a bivariate risk model with type II bivariate generalized power series Poisson model as the counting process. For this model we derive distribution of the time to ruin and bounds for the probability of ruin. We obtain partial integro-differential equation for the ruin probabilities and express its bivariate transform through two univariate boundary transforms,where one of the initial capitals is fixed at zero.

CO2, CH4 and CO are the most critical atmospheric gases in terms of their impact on the radiative system, air quality and health. This work provides information on the direction of source areas and potential sources of emissions and shows many aspects of these gases by a statistical analysis using bivariate polar diagrams and local weather conditions (e.g., temperature, wind speed and wind direction) recorded at the Lamto station (LTO, 6°31N and 5°02W) in Côte d’Ivoire over the 2014-2018 period. The results show that the main regions contributing to the high concentrations of CH4 (> 1925 ppb) and CO2 (> 420 ppm) in the GSS, GSP, PSS and PSP seasons are the North and Northwest sectors of Lamto. In these directions, CH4 and CO2 concentrations are associated with wind speeds less than 6 m.s-1, due to the influences of local sources as emissions resulting from the degradation of organic matter submerged during the impoundment of the Taabo dam, and/nor human activities linked to the practice of intensive agriculture. In addition, the high concentrations of CO (> 350 ppb) are observed in GSS in the North, North-West, North-East and East sectors for wind speeds less than or equal to 9 m.s-1, due to the influences of both local and distant sources. The correlation coefficients between CH4 and CO, and between CH4 and CO2 are positive and significant in all sectors. However, those calculated between CO2 and CO have showed both low and high values in all seasons.

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.

In this paper, we make research on fractal characteristics of the superposition of fractal surfaces in the view of fractal dimension. We give the upper bound of the lower and upper Box dimension of the graph of the sum of two bivariate continuous functions and calculate the exact values of them under some particular conditions. Further, it has been proved that the superposition of two continuous surfaces cannot keep the fractal dimensions invariable unless both of them are two-dimensional. A concrete example of numerical experiment has been provided to verify our theoretical results. This study can be applied to the fractal analysis of metal fracture surfaces or computer image surfaces.

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér-von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes.

A copula is a useful tool for constructing bivariate and/or multivariate distributions. In this article, we consider a new modified class of (Farlie-Gumbel-Morgenstern) FGM bivariate copula for constructing several dierent bivariate Kumaraswamy type copulas and discuss their structural properties, including dependence structures. It is established that construction of bivariate distributions by this method allows for greater flexibility in the values of Spearman's correlation coefficient rho,  and Kendall's tau . For illustrative purposes, one representative data set is utilized to exhibit the applicability of these proposed bivariate copula models.

Splines and quasi-interpolation operators are important both in approximation theory and applications. In this paper, we construct a family of quasi-interpolation operators for the bivariate quintic spline spaces S₅³ (∆_mn⁽²⁾). Moreover, the properties of the proposed quasi-interpolation operators are studied, as well as its applications for solving two-dimensional Burgers’ equation and image reconstruction. Some numerical examples show that these methods, which are easy to implement, provide accurate results.

This paper presents the symmetries of differential equations associated with one-variable and Bivariate Hermite polynomials by proposing a representation of Lie algebra for these differential operators. Applying the Baker-Campbell-Hausdorff formula to these algebras, results in new relations and generating functions in one-variable and Bivariate Hermite polynomials. A general form of representation for other orthogonal polynomials such as Laguerre polynomials is introduced.

This paper surveys estimates of the transmission features of the novel coronavirus, and then proposes a model to address sample-selection bias in estimated determinants of infection. Containment assumptions of the infection forecasting models depend on assumed effects of policies and self-regulating behavior. In the commons dilemma of the pandemic, the perceived ‘low risks’ of unregulated marginal choices do not reflect the full social cost, implying non-pharmaceutical interventions (NPI) to reduce mortality can enhance social welfare. As more economic activity renews with liftings of restrictive NPI (RNPI), a critical question concerns the ability of milder NPI (MNPI) and voluntary precautions to mitigate the risk of greater infections and deaths while also limiting the pandemic’s economic damage and its social costs. Ineffective NPI could lead to continued COVID-19 waves and new types of crises, worsened expectations and delayed economic recoveries. From the central range of surveyed estimates of transmission and alternative herd-immunity-threshold estimates, a ‘worst-case’ virus guidepost suggests eventual deaths of around 25 to 41 million worldwide and 1.1 to 1.7 million in the U.S. needed to reach herd immunity with no vaccine or treatment. The most optimistic study surveyed (theoretical model from a non-reviewed preprint study) combined with the low end of the range of the estimated mortality rate suggests 6 to 9 million deaths worldwide and 250 to 370 thousand in the U.S. to reach herd immunity. Successes in the mix of NPI, treatments, and vaccine can limit the eventual global death toll of the virus. Improved estimation models for forecasting and decision making may assist in better targeting the local timings and mix of NPI. Diagnostic tests for the virus have been largely limited to symptomatic cases, causing possible sample selection bias. A recursive bivariate probit model of infection and testing is proposed along with several possible applications from cross-section or panel-data estimation. Multiple potential explanatory variables, data sources, and estimation needs are specified and discussed.

The philosophy of testing statistical hypothesis is a natural consequence and functional extension of mathematical analysis of Probability. Along with the concept of recurrence when applied to random sequences and functions, it leads to the analysis of a priori and posterior which implies testing statistical hypothesis. Testing statistical hypothesis also involves algebraic, functional and dimensional considerations, which are found in the works of Laplace. Aspects of mathematical analysis such as universality of solutions, Laws of Large Numbers, Entropy, Information, and various functional dependencies are the main factors explained in the five properties that lead to implication of testing statistical hypothesis. Various interesting examples with modern scientific significance from genetics, astrophysics, and other areas give methodological access to answers of different problems and phenomena which are involved in the logic of testing statistical hypothesis.

In light of the current situation where no testing equipment is available for measuring thermal deformation of objects, this paper proposes a novel method for accurate and precise measurement. The method overcomes the limitations of previous approaches that relied on pitch angle. By utilizing the principle of biplane multiple reflections, a bivariate laser spot displacement analysis algorithm is devised to attain highly precise measurements of bivariate angles. Additionally, a temperature gradient comparison algorithm is introduced to calculate the indicator test results under specific temperature conditions. To validate the effectiveness and reliability of this method, a testing system is constructed and utilized. The results demonstrate that the thermal deformation angle change test achieves an impressive accuracy of 0.015″ and a rate of thermal deformation angle change of 0.3247″/°C. These values are in close agreement with the previously simulated analysis result of 0.359″/°C, with only a relative error of 9.55%. Therefore, the test results confirm the efficacy and reliability of this testing method along with the feasibility of the algorithm processing.

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.