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Preprint ARTICLE | doi:10.20944/preprints202306.0397.v1

A New EWMA Control Chart for Monitoring Multinomial Proportions

Su-Fen Yang, Shengjin Gan, Li-Pang Chen

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Control chart; Multinomial distribution; specification limits; Pearson χ^(2 )statistic

Online: 6 June 2023 (07:45:37 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.0098.v1

Dirichlet Process Log Skew-normal Mixture with Missing at Random Covariate in Insurance Claim Analysis

Minkun Kim, David Lindberg, Martin Crane, Marija Bezbradica

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Bayesian nonparametric model; heterogeneity; missing at random; log-normal sum approximation; aggregate insurance claims; clustering; generative model

Online: 1 June 2023 (13:47:57 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.1166.v2

Constructing Optimal Designs for Order-of-Addition Experiments Using a Hybrid Algorithm

Dongying Wang, Sumin Wang

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Pairwise-order model; D-optimal; A-optimal; M.S.-optimal; particle swarm optimization; Fedorov exchange algorithm

Online: 31 May 2023 (08:45:18 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.2118.v1

Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited

Alexander Veretennikov

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: stochastic differential equation; gradient type drift; polynomial recurrence

Online: 30 May 2023 (10:44:05 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1878.v1

Randomly Stopped Sums with Generalized Subexponential Distribution

Jūratė Karasevičienė, Jonas Siaulys

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: subexponentiality; generalized subexponentiality; heavy tail; randomly stopped sum

Online: 26 May 2023 (07:33:51 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1198.v1

Heavy-Tailed Probability Distributions: Some Examples of Their Appearance

Lev b. Klebanov, Yulia V. Kuvaeva, Svetlozar T Rachev

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: heavy-tailed distributions; Pareto law; Lotka law; Zipf law; probability generating function.

Online: 17 May 2023 (05:41:04 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1175.v1

Small Values and Chung's Laws of the Iterated Logarithm for Spatial Surface of Operator Fractional Brownian Motion

Wensheng Wang

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: operator fractional Brownian motion; small ball probability; operator self-similarity; Chung's law of the iterated logarithm

Online: 17 May 2023 (03:38:22 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1037.v1

Bayesian Estimations of Shannon Entropy and Rényi Entropy of Inverse Weibull Distribution

Haiping Ren, Xue Hu

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Inverse Weibull distribution; symmetric entropy loss function; Rényi entropy; Bayesian estimation; Lindley approximation

Online: 15 May 2023 (11:14:14 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0904.v1

Quick and Complete Convergence in the Law of Large Numbers with Applications to Statistics

Alexander Tartakovsky

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Complete convergence; r-quick convergence; sequential analysis; hypothesis testing; changepoint detection

Online: 12 May 2023 (08:25:35 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0716.v1

Correlations in Compositional Data without Log-Transformations

Yury Monich, Yury Nechipurenko

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: compositional data; mathematical expectation shift; loss of degrees of freedom; hybrid model

Online: 10 May 2023 (08:57:50 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0583.v1

Fractional Equations for the Scaling Limits of L’evy Walks With Position Depending Jump Distributions

Vassili N. Kolokoltsov

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: L´evy walks; fractional equations of variable order; Caputo-Dzherbashian and Riemann-Liouville derivatives; material fractional derivatives; scaling limit; continu-ous time random walks (CTRW); subordinated Markov processes

Online: 9 May 2023 (07:27:22 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.1166.v1

Constructing Optimal Designs for Order-of-Addition Experiments Using a Hybrid Algorithm

Dongying Wang, Sumin Wang

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Pairwise-order model; D-optimal; A-optimal; M.S.-optimal; particle swarm optimization; Fedorov exchange algorithm

Online: 28 April 2023 (10:43:27 CEST)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202302.0367.v11

Defining the Most Generalized, Natural Extension of the Expected Value on Measurable Functions

Bharath Krishnan

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Prevalence; Expected Value; Uniform Measure; Measure theory; Uniform Cover; Entropy; Sample; Linear; Superlinear; Choice Function; Bernard's Paradox; Pseudo-random

Online: 26 April 2023 (03:35:26 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0360.v1

High-Dimensional Variable Selection for Quantile Regression based on Variational Bayesian Method

Dengluan Dai, Anmin Tang, Jinli Ye

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: quantile regression; Spike-and-Slab prior; variational Bayesian; high-dimensional data

Online: 14 April 2023 (09:36:47 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0217.v1

Structural Change-Point Detection for Time Series via Support Vector Regression and Self-Normalization Method

Zhanshou CHEN, Nini Mrs. XIE

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: SVR-ARMA model; Change-point; Self-normalization test; Structural change-point

Online: 11 April 2023 (09:41:04 CEST)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202302.0367.v10

Defining the Most Generalized, Natural Extension of the Expected Value on Measurable Functions

Bharath Krishnan

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Prevalence; Expected Value; Uniform Measure; Measure theory; Uniform Cover; Entropy; Sample; Linear; Superlinear; Choice Function; Bernard's Paradox; Pseudo-random

Online: 7 April 2023 (05:16:10 CEST)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202302.0367.v9

Defining the Most Generalized, Natural Extension of the Expected Value on Measurable Functions

Bharath Krishnan

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Prevalence; Expected Value; Uniform Measure; Measure theory; Uniform Cover; Entropy; Sample; Linear; Superlinear; Choice Function; Bernard's Paradox; Pseudo-random

Online: 6 April 2023 (10:04:39 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202303.0320.v1

Flood Frequency Analysis Using the Gamma Family Probability Distributions

Cornel Ilinca, Cristian Gabriel Anghel

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Kritsky-Menkel; Pearson; Wilson-Hilferty; Chi; Inverse Chi; Pseudo-Weibull; estimation parameters; corrected parameters; approximate form; method of ordinary moments; method of linear moments; the method of least squares; confidence interval

Online: 17 March 2023 (09:23:31 CET)

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Preprint ARTICLE | doi:10.20944/preprints202303.0154.v1

Bertrand Paradox: Critical Consideration of Two of the Three Solutions in Terms of Geometry

Pavel Brazhnikov

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Bertrand paradox; geometric probability; probability estimation method

Online: 8 March 2023 (10:10:49 CET)

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Preprint ARTICLE | doi:10.20944/preprints202302.0520.v1

Multilevel Functional Principal Components Analysis Presents a Viable Method of Modelling Dynamical Shape Changes

Damian Joseph John Farnell1, Peter Claes

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Multilevel Functional Principal Components Analysis (mFPCA); Dynamical Shape Changes

Online: 28 February 2023 (11:29:22 CET)

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Preprint ARTICLE | doi:10.20944/preprints202302.0383.v1

Modelling Socioeconomic Determinants of Building Fires through Backward Elimination by Robust Final Prediction Error Criterion

Albertus Untadi, Lily D Li, Michael Li, Roland Dodd

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Building fire; Socioeconomic determinants; South East Queensland; Predictive model; Forecasting; Backward elimination; Robust final predictor error

Online: 22 February 2023 (09:37:47 CET)

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Preprint ARTICLE | doi:10.20944/preprints202302.0229.v1

Branching Random Walks with One Particle Generation Center and Possible Absorption at Every Point

Elena Filichkina, Elena Yarovaya

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: branching random walks; moments of particle numbers; evolution operator; Green’s function

Online: 14 February 2023 (03:29:07 CET)

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Preprint ARTICLE | doi:10.20944/preprints202302.0213.v1

dbs: Stata Command to Compute Double Bootstrap Confidence Intervals

Felix Bittmann

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: bootstrapping; confidence intervals; dbs; resampling; variance estimation; heteroscedasticity

Online: 13 February 2023 (09:50:08 CET)

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Preprint ARTICLE | doi:10.20944/preprints202301.0524.v1

Statistical Inference for Finite Mixture of Matrix Variate t-distribution

Xinyu Yang, Leigang Dong, Zhichuan Zhu, Weisan Wu

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Matrix variate distribution; Mixture models; EM-algorithm; Penalized likelihood

Online: 28 January 2023 (08:53:19 CET)

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Preprint ARTICLE | doi:10.20944/preprints202301.0423.v1

Confidence Intervals and Regions for Proportions Under Various Three-Endmember Linear Mixture Models

Mark Berman

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: proportion estimation; linear mixture model; confidence interval; confidence region; photosynthetic vegetation; non-photosynthetic vegetation; soil; Landsat Thematic Mapper

Online: 24 January 2023 (05:56:10 CET)

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Preprint ARTICLE | doi:10.20944/preprints202212.0488.v1

Evaluating State-Level Prescription Drug Monitoring Program (PDMP) and Pill Mill Effects on Opioid Consumption in Pharmaceutical Supply Chain

Amirreza Sahebi Fakhrabad, Amir Hossein Sadeghi, Robert Handfield

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Opioid crisis; PDMP; Pill Mill; Difference-in-Difference; Policy Analysis; Pharmaceutical Supply Chain

Online: 26 December 2022 (11:10:57 CET)

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Preprint ARTICLE | doi:10.20944/preprints202212.0474.v1

Delicate Comparison of the Central and Non-central Lyapunov Ratios with Applications to the Berry–Esseen Inequality for Compound Poisson Distributions

Vladimir Makarenko, Irina Shevtsova

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Lyapunov fraction; extreme problem, moment inequality; central limit theorem; Berry–Esseen inequality; compound Poisson distribution; normal approximation

Online: 26 December 2022 (06:43:46 CET)

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Preprint ARTICLE | doi:10.20944/preprints202212.0325.v1

Improved CUSUM Schemes for Monitoring Processes Mean

Ganiyu Ayodele Ajibade, Opeyemi Oluwole Enoch

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: CUSUM; fast initial response; generalized fast initial response (GFIR); average run length (ARL)

Online: 19 December 2022 (04:43:21 CET)

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Preprint ARTICLE | doi:10.20944/preprints202212.0072.v1

A New Statistical Model Based on the Novel Generalized Odd Beta Prime Family of Continuous Probability Distributions with Applications to Cancer Disease Data Sets

Ahmad Abubakar Suleiman, Mahmod Othman, Aliyu Ismail Ishaq, Mohd Lazim Abdullah, Rachmah Indawati, Hanita Daud, Rajalingam Sokkalingam

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: beta prime distribution; Weibull distribution; mixture representations; information generating function; entropies; order statistics; Monte Carlo simulation; blood cancer disease

Online: 5 December 2022 (09:47:54 CET)

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Preprint ARTICLE | doi:10.20944/preprints202212.0024.v1

Indexing Inefficacy of Efforts to Stop Escalation of COVID Mortality

Ram Shanmugam, Lawrence Fulton, Jose Betancourt, Gerardo J Pacheco

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Positive Poisson distribution, Under dispersion, Bayesian analysis, prediction, index of infectivity.

Online: 1 December 2022 (10:25:33 CET)

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Preprint ARTICLE | doi:10.20944/preprints202211.0419.v1

Samurai Survival Statistics: A Monte-Carlo Approach to Game-Theoretical Sudden Death Interactions

Paulo Garcia

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Samurai; Miyamoto Musashi; Monte-Carlo; Markov; Probability

Online: 22 November 2022 (10:11:05 CET)

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Preprint ARTICLE | doi:10.20944/preprints202210.0474.v1

Uncertainty Assessment of Flood Hazard due to Levee Breaching

Cédric Goeury, Vito Bacchi, Fabrice Zaoui, Sophie Bacchi, Sara Pavan, Kamal El kadi Abderrezzak

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: flood hazard; dike breach; Monte Carlo framework; Global Sensitivity Analysis

Online: 31 October 2022 (08:46:28 CET)

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Preprint ARTICLE | doi:10.20944/preprints202210.0430.v1

Four-Parameter Guessing Model and Related Item Response Models

Alexander Robitzsch

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: item response model, four-parameter guessing model, guessing effects, multiple-choice items

Online: 27 October 2022 (09:50:46 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202210.0169.v1

Minimax Lower Bounds for High-Dimensional Multi-Response Errors-in-Variables Regression

Xin Li, Dongya Wu

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: low-rank matrices; errors-in-variables models; lower bounds; Kullback-Leibler divergence; information-theoretic limitations

Online: 12 October 2022 (09:57:25 CEST)

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Preprint ESSAY | doi:10.20944/preprints202210.0085.v1

Using Directed Acyclic Graphs (Dags) to Represent the Data Generating Mechanisms of Disease and Healthcare Pathways: A Guide for Educators, Students, Practitioners and Researchers

George Ellison

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Directed Acyclic Graph; DAG; confounding; collider bias; epistemology; inferential statistics

Online: 8 October 2022 (02:59:34 CEST)

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Directed acyclic graphs (DAGs) are nonparametric causal path diagrams that have substantial utility as principled representations of disease and healthcare pathways, and of the underlying ‘data generating mechanisms’ these pathways involve. As such, DAGs provide a valuable bridge between: the aetiological knowledge, operational insight and professional experience on which clinical training and practice depend; and the more abstract epistemological and analytical considerations required to extract robust statistical insight from health and healthcare data. DAGs are nonetheless vulnerable to imperfect biomedical paradigms, partial clinical knowledge and limited empirical data. DAGs drawn under such circumstances offer limited scope for statistical insight free from cognitive, analytical or inferential bias if: they misrepresent the data generating mechanisms involved; or ignore the important role that omitted variables (whether measured, unmeasured or unacknowledged) might play therein. To address these weaknesses and broaden the appeal and application of DAGs, this chapter provides ten simple steps that educators can use to improve the analytical competence and statistical confidence of the healthcare students, qualified practitioners and experienced researchers they support. These steps use temporal logic to draw DAGs so as to: reduce reliance on uncertain knowledge, incomplete information, flawed assumptions or guesswork; and avoid, mitigate or acknowledge the errors and biases that each of these incur. The chapter comprises an accessible, non-technical overview of the perspective and thoughtfulness required to generate temporally coherent DAGs as objective representations of the probabilistic causal paths involved in context-specific data generating mechanisms. It encourages a focus on those variables operating as potential sources of analytical or inferential bias when estimating the plausible, probabilistic causal relationship between two pre-specified variables; and specifically addresses the challenges posed by: omitted; time-variant; non-asynchronous; and temporally obscure variables. The chapter includes a worked example based on a published clinical study to demonstrate how each of the steps required to generate temporally-informed DAGs can be applied to: critically appraise the analytical decisions made during applied healthcare research; and inform the decisions required when designing, undertaking and analysing primary and secondary, prospective and retrospective research. The appendices include a summary of ten recommendations for improving the reporting and interrogability of DAGs and DAG-informed analyses.

Preprint ARTICLE | doi:10.20944/preprints202209.0425.v1

Manfred Deistler and the General Dynamic Factor Model Approach to the Analysis of High-Dimensional Time Series

Marc Hallin

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: High-dimensional time series; General Dynamic Factor Models; spiked covariance model; reduced-rank process; singular spectrum.

Online: 28 September 2022 (02:02:26 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0277.v1

Early Retrieval Problem and Link Prediction Evaluation via the Area Under the Magnified ROC

Alessandro Muscoloni, Carlo Vittorio Cannistraci

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: link prediction; AUC-ROC; Early retrieval evaluation

Online: 19 September 2022 (10:31:53 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0252.v1

Fundamentally Good Alternative to Normal Distribution

Kabir Bindawa Abdullahi

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: alternative parameterization; normal distribution; dispersion estimators; location-invariance; scale-invariance; scale-and-location-invariance

Online: 19 September 2022 (02:06:09 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0231.v1

Evidence-Based Regularization for Neural Networks

Giuseppe Nuti, Andreea-Ingrid Cross, Philipp Rindler

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: neural networks; regularization; deep networks

Online: 15 September 2022 (13:06:13 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202208.0234.v1

Variational Bayesian Approximation (VBA): A comparison between three optimization algorithms

Seyedeh Azadeh Fallah Mortezanejad, Ali Mohammad-Djafari

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Variational Bayesian Approach (VBA); Kullback–Leibler Divergence; Mean Field Approximation (MFA); Optimization Algorithm

Online: 12 August 2022 (10:26:02 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202208.0179.v1

Measurement Uncertainty Interval In Case of a Known Relationship between Precision and Mean

Steffen Uhlig, Bertrand Colson, Petra Gowik

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: In-house validation study; reproducibility precision; measurement uncertainty; prediction interval; uncertainty interval

Online: 9 August 2022 (10:56:40 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0357.v1

A Comprehensive Analysis of Proportional Intensity-based Software Reliability Models with Covariates

Siqiao Li, Tadashi Dohi, Hiroyuki Okamura

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: software reliability models; proportional intensity model; non-homogeneous Poisson process; time-dependent covariate; maximum likelihood estimation; goodness-of-fit performance; predictive performance

Online: 25 July 2022 (08:13:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0323.v1

Low Complexity, Low Probability Patterns and Consequences for Algorithmic Probability Applications

Mohamed Alaskandarani, Kamaludin Dingle

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Algorithmic probability; Kolmogorov complexity; prediction; induction

Online: 21 July 2022 (10:48:26 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0032.v1

Twisted Wang Transform Distribution

Frank Wang

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: twisted Wang transform; shape factor; EP curve; reinsurance; numerical optimization

Online: 4 July 2022 (05:08:29 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0342.v1

Uniform Test on the Mixture Simplex Region

Haiqing Zhao, Guanghui Li, Junpeng Li

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: mixture experiments; lattice point sets; uniform designs

Online: 27 June 2022 (03:09:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0009.v1

Skew Counterparts of the Generalized Double Lomax Distribution: Properties and Applications

Ievgen Turchyn

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Generalized double Lomax distribution; exponentiated distribution; maximum likelihood; moment; entropy

Online: 1 June 2022 (09:43:10 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0064.v1

Is the Probability of Tossing a Coin Really 50-50%?

Vladimir Pletser

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: coin toss; probability; impact

Online: 6 May 2022 (09:03:42 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0049.v1

Algebraic Treatments of a General Linear Model With Adding-up Restrictions

Yongge Tian

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: General linear model; adding-up restrictions; estimability; OLSE; BLUE

Online: 5 May 2022 (16:05:37 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0295.v1

Benchmark of Holt-Winters and SARIMA Methods in Predicting Jakarta Climate

Amartya Natayu, Quincy Julian H. Clarke, Muhamad Fikri

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Forecasting; SARIMA; Holt-Winters; Climate; Big Data

Online: 29 April 2022 (08:44:28 CEST)

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Preprint COMMUNICATION | doi:10.20944/preprints202203.0243.v2

The Wasps are Clever: Keeping Out and Finding Bot Answers in Internet Surveys Used for Health Research

Julii Brainard, Anne Killett, Julie Houghton, Diane Bunn, Laura Watts, Suzanne Mumford, Sarah J. O'Brien, Kathleen Lane

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: data analysis; surveys and questionnaires; internet; social class

Online: 13 April 2022 (06:32:09 CEST)

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Preprint REVIEW | doi:10.20944/preprints202203.0338.v1

COVID-19 Test Frequency Versus Test Sensitivity in Disrupting SARS-CoV-2 Transmission: A Review of Statistical Modeling Simulations

Justin Rogers, Laurel Jackson, Adam Buss, Susan Gawel

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: COVID-19; rapid testing; test sensitivity; test frequency; testing programs; compartmental models

Online: 25 March 2022 (03:50:14 CET)

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Preprint REVIEW | doi:10.20944/preprints202112.0235.v2

Why and How We Should Join the Shift From Significance Testing to Estimation

Daniel Berner, Valentin Amrhein

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Compatibility interval; effect size; null hypothesis; p-value; statistical inference

Online: 23 March 2022 (09:30:28 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202203.0243.v1

The Wasps are Clever: Keeping Out and Finding Bot Answers in Internet Surveys Used for Health Research

Julii Brainard, Kathleen Lane, Laura Watts, Diane Bunn

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: data analysis; surveys and questionnaires; internet; social class

Online: 17 March 2022 (04:02:29 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0206.v1

Machine Learning in Ratemaking, an Application in Commercial Auto Insurance

Spencer Matthews, Brian Hartman

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Ratemaking; Machine Learning; Explainability; Auto Insurance

Online: 15 March 2022 (10:59:32 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0182.v1

Ordinalbayes: Fitting Ordinal Bayesian Regression Models to High-Dimensional Data Using R

Kellie J. Archer, Anna Eames Seffernick, Shuai Sun, Yiran Zhang

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: cumulative logit; penalized models; LASSO; variable inclusion indicators; spike-and-slab

Online: 14 March 2022 (10:04:52 CET)

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Preprint TECHNICAL NOTE | doi:10.20944/preprints202203.0166.v1

A Note on Novel Normal-Power Non-Linear Function

Matthew Iwada Ekum

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Bimodal Dependent Variable; Normal-Power; Non-Linear; Least Square Estimation; Economy-Tourism Model

Online: 11 March 2022 (10:07:40 CET)

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Preprint ARTICLE | doi:10.20944/preprints202202.0322.v1

A Generalized Measure of Cumulative Residual Entropy

Sudheesh Kumar Kattumannil, E. P. Sreedevi, N. Balakrishnan

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: cumulative entropy; cumulative residual entropy; extropy; gini mean difference; tsallis entropy; weighted cumulative residual entropy

Online: 25 February 2022 (04:44:39 CET)

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Preprint ARTICLE | doi:10.20944/preprints202202.0230.v1

Bayesian Smoothing Splines

Gary Venter

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: smoothing splines; shrinkage priors; MCMC; Bayesian methods

Online: 18 February 2022 (09:30:41 CET)

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Preprint ARTICLE | doi:10.20944/preprints202202.0150.v1

IoT-Orchestration based Nanogrid Energy Management System and Optimal Time-Aware Scheduling for Efficient Energy Usage in Nanogrid

Faiza Qayyum, Harun Jamil, Faisal Jamil, Shabir Ahmed, Do-Hyeun Kim

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Internet of things; complex problem solving; Critical IoT systems; Microgrid; Nanogrid; Optimization; Scheduling; Task modeling; Task orchestration

Online: 10 February 2022 (11:00:39 CET)

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The present era of the Internet of Things (IoT) having intelligent functionalities in solving problems pertaining to realtime mission-critical systems has brought an immense revolution in diverse fields including healthcare and navigation systems. However, to the best of our knowledge, the potential of IoT has not been fully exploited yet in the field of the energy sector. We argue that there is an immense need to shift the traditional mission-critical electric power system architecture to IoT-based fully orchestrated architecture in order to increase efficiency, as billions of investment is reserved for the energy sector globally. Since network orchestration deals with auomating the interaction between multiple components involved to execute a particular service, therefore, scheduling the relevant processes within strict deadlines becomes the core pillar of the architecture. The mission-critical systems with urgent task execution often suffer from issues of missing task deadlines. In this study, we present a novel IoT task orchestration architecture for efficient energy management of a nanogrid system that focuses on minimizing the use of nonrenewable energy resources and maximizing the use of renewable energy resources. Moreover, major components of IoT task orchestration such as task mapping and task scheduling are also enhanced using NLP and PSO optimization modules. The proposed task scheduling algorithm incorporates the optimized surplus time, and efficiently executes the energy management-related tasks contemplating to their types. The study utilizes sensors to obtain data from physical IoT devices, including photovoltaic (PV), Energy Storage System (ESS), and diesel generator (DG). The performance of the proposed model is evaluated using data set of nanogrid houses. The outcomes revealed that IoT-task orchestration has played a pivotal role in efficient energy management for nanogrid mission-critical system. Furthermore, the comparison with state-of-the-art scheduling algorithms showed that the task starvation rate is reduced to 16% and 12% when compared with RR and FEF algorithms, respectively.

Preprint ARTICLE | doi:10.20944/preprints202202.0081.v1

Online Anomaly Detection for Smartphone-Based Multivariate Behavioral Time Series Data

Gang Liu, Jukka-Pekka Onnela

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Online learning; Anomaly detection; Hotelling’s T-squared test; Digital phenotyping

Online: 7 February 2022 (11:54:54 CET)

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Preprint REVIEW | doi:10.20944/preprints202201.0407.v1

Bayesian Nonlinear Models for Repeated Measurement Data: An Overview, Implementation, and Applications

Se Yoon Lee

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Bayesian nonlinear hierarchical model; Bayesian nonlinear mixed effects models; Inter-individual variation; Intra-individual variation; Markov chain Monte Carlo technique

Online: 27 January 2022 (04:55:25 CET)

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Preprint ARTICLE | doi:10.20944/preprints202201.0165.v1

Prevalence, Risk Factors and Residential Variation among HIV/TB co-infected Mortality in Amhara Region, Fenote Selam Hospital: Application of Multilevel Logistic Regression

Berhanu Bekele Debelu

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: HIV/TB co-infected Mortality; Residential Variations; Multilevel Logistic Regression

Online: 12 January 2022 (13:34:06 CET)

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Preprint ARTICLE | doi:10.20944/preprints202201.0160.v1

An Exploration of Pathologies of Multilevel Principal Components Analysis in Statistical Models of Shape

Damian JJ Farnell

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Multilevel Principal Components Analysis (mPCA); 3D shape analysis; Monte Carlo simulations

Online: 12 January 2022 (10:44:23 CET)

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3D facial surface imaging is a useful tool in dentistry and in terms of diagnostics and treatment planning. Between-groups PCA (bgPCA) is a method that has been used to analyse shapes in biological morphometrics, although various “pathologies” of bgPCA have recently been proposed. Monte Carlo (MC) simulated datasets were created here in order to explore “pathologies” of multilevel PCA (mPCA), where mPCA with two levels is equivalent to bgPCA. The first set of MC experiments involved 300 uncorrelated normally distributed variables, whereas the second set of MC experiments used correlated multivariate MC data describing 3D facial shape. We confirmed previous results of other researchers that indicated that bgPCA (and so also mPCA) can give a false impression of strong differences in component scores between groups when there is none in reality. These spurious differences in component scores via mPCA reduced strongly as the sample sizes per group were increased. Eigenvalues via mPCA were also found to be strongly effected by imbalances in sample sizes per group, although this problem was removed by using weighted forms of covariance matrices suggested by the maximum likelihood solution of the two-level model. However, this did not solve problems of spurious differences between groups in these simulations, which was driven by very small sample sizes in one group here. As a “rule of thumb” only, all of our experiments indicate that reasonable results are obtained when sample sizes per group in all groups are at least equal to the number of variables. Interestingly, the sum of all eigenvalues over both levels via mPCA scaled approximately linearly with the inverse of the sample size per group in all experiments. Finally, between-group variation was added explicitly to the MC data generation model in two experiments considered here. Results for the sum of all eigenvalues via mPCA predicted the asymptotic amount for the total amount of variance correctly in this case, whereas standard “single-level” PCA underestimated this quantity.

Preprint ARTICLE | doi:10.20944/preprints202112.0427.v1

The SAMME.C2 Algorithm for Severely Imbalanced Multi-class Classification

Banghee So, Emiliano A. Valdez

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: AdaBoost; Cost-sensitive learning; Forward stagewise additive modeling; SAMME; SAMME.C2; SMOTE

Online: 27 December 2021 (12:12:54 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0324.v1

On a Problem of Infinite Divisibility

Lev Klebanov

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: characteristic function; infinite divisibility; singularities

Online: 21 December 2021 (12:01:39 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0323.v1

Optimization of Intrusion Detection Systems Determined by Ameliorated HNADAM-SGD Algorithm

Shyla Shyla, Vishal Bhatnagar, Vikram Bali, Shivani Bali

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Intrusion Detection System (IDS); HNADAM-SDG(Hybrid Nestrov-Accelerated Adaptive Moment Estimation –Stochastic Gradient Descent); Network-based Intrusion Detection System (NIDS); Host-based Intrusion Detection System (HIDS); Signature-based Intrusion Detection System (SIDS); Anomaly-based Intrusion Detection System (AIDS); Algorithms; Machine Learning.

Online: 21 December 2021 (11:45:39 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0298.v1

Ruin Probabilities and Complex Analysis

Andrew Leung

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: reserves; ruin probability in infinite continuous time, Lebesgue spaces; Fourier Transform; Inverse Fourier Transform; analytic functions; Cauchy’s Theorem

Online: 20 December 2021 (09:47:46 CET)

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Preprint REVIEW | doi:10.20944/preprints202112.0235.v1

Why and How We Should Join the Shift From Significance Testing to Estimation

Daniel Berner, Valentin Amrhein

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Compatibility interval; effect size; null hypothesis; p-value; statistical inference

Online: 14 December 2021 (12:47:07 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0535.v1

On the ROC Area of Ensemble Forecasts for Rare Events

Zied Ben Bouallegue, David S. Richardson

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: ROC area; discrimination; verification artefacts; trapezoidal approximation; bi-normal model; imprecise probability

Online: 29 November 2021 (12:36:55 CET)

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Preprint REVIEW | doi:10.20944/preprints202111.0310.v1

A Literature Review of Semi-functional Partial Linear Regression Models

Mohammad Fayaz

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Functional Data Analysis (FDA); Hybrid Data; Semi-Functional Partial Linear Regression Model (SFPLR); Partial Functional Linear Regression; Literature Review

Online: 17 November 2021 (15:21:19 CET)

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Preprint REVIEW | doi:10.20944/preprints202111.0291.v1

Valuing the Future, Discounting in Random Environments: A Review

Jaume Masoliver, Miquel Montero, Josep Perelló, J. Doyne Farmer, John Geanakoplos

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: stochastic processes; finance; interest rates

Online: 16 November 2021 (13:50:41 CET)

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Preprint ARTICLE | doi:10.20944/preprints202105.0117.v2

Near-Optimal Sparse Neural Trees for Supervised Learning

Tanujit Chakraborty

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: decision trees; deep feed-forward network; neural trees; consistency; optimal rate of convergence

Online: 9 November 2021 (16:54:30 CET)

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Preprint ARTICLE | doi:10.20944/preprints202110.0362.v1

Effects of Different Parameter Settings for 3D Data Smoothing and Mesh Simplification on Towards Near Real-Time 3D Reconstruction of High Resolution Bioceramic Bone Void Filling Medical Images

Daniel Jie Yuan Chin, Ahmad Sufril Azlan Mohamed, Khairul Anuar Shariff, Mohd Nadhir Ab Wahab, Kunio Ishikawa

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: 3D reconstruction; 3D data smoothing; mesh simplification; high resolution micro-CT images

Online: 25 October 2021 (15:34:27 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0049.v2

Minimum Message Length in Hybrid ARMA and LSTM Model Forecasting

Zheng Fang, David L. Dowe, Shelton Peiris, Dedi Rosadi

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: long short-term memory; minimum message length; time series; neural network; deep learning; Bayesian statistics; probabilistic modeling

Online: 12 October 2021 (11:41:30 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0049.v1

Minimum Message Length in Hybrid ARMA and LSTM Model Forecasting

Zheng Fang, David L. Dowe, Shelton Peiris, Dedi Rosadi

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: long short-term memory; minimum message length; time series; neural network; deep learning; Bayesian statistics; probabilistic modeling

Online: 4 October 2021 (11:11:33 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0042.v1

Super RaSE: Super Random Subspace Ensemble Classification

Jianan Zhu, Yang Feng

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: classification; ensemble; subspace; sparsity; feature ranking

Online: 4 October 2021 (10:36:37 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0526.v1

Monitoring the Nonconforming Fraction with a Dynamic Scheme When Sample Sizes are Time-varying

Víctor Hugo Morales, Carlos Arturo Panza, Javier Blanco

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Average run length; binomial distribution; control charts; EWMAG control chart; nonconforming fraction; p control chart; Phase II; SPC

Online: 30 September 2021 (15:30:52 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0460.v1

Deterministic Sampling from Univariate Normal Distributions with Sierpinski Space-Filling Curves

Hime Oliveira

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Space-filling curves; Ergodic Theory; random number generation; Gaussian distribution

Online: 28 September 2021 (09:56:55 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202105.0277.v2

Lagged Covariance and Cross-Covariance Operators of Processes in Cartesian Products of Abstract Hilbert Spaces

Sebastian Kühnert

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Estimation; functional time series; lagged covariance operator; lagged cross covariance operator; principle components

Online: 10 September 2021 (11:05:11 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0021.v1

Revisiting Statistics and Evidence-Based Medicine: On the Fallacy of the Effect Size Based on Correlation and Misconception of Contingency Tables

Sergey Roussakow

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Effect size; correlation coefficient; association measure; covariance; mean square contingency coefficient; mean square effect half-size; Pearson’s Phi; 2 × 2 table; binary crosstab; gross crosstab; contingency table

Online: 1 September 2021 (14:28:47 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0523.v1

The Distributions of Sums for Shanker, Akash, Ishita, Pranav, Rani, and Ram Awadh

Afshin Yaghoubi

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Akash distribution; Ishita distribution; Pranav distribution; Ram Awadh distribution; Rani ‎distribution; Shanker distribution

Online: 27 August 2021 (13:55:49 CEST)

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Preprint REVIEW | doi:10.20944/preprints202108.0521.v1

The Costs and Potential Benefits of Introducing the “I Don’t Know” Answer in Binary Classification Settings

Damjan Krstajic

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: non-applicability domain; binary classification; ignorance; decision-making

Online: 27 August 2021 (13:05:02 CEST)

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Working Paper ARTICLE

Entropy and Wealth

Demetris Koutsoyiannis, G.-Fivos Sargentis

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: entropy; wealth; income distribution; options; potentiality; principle of maximum entropy; Second Law; stochastics

Online: 18 August 2021 (08:14:33 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0248.v1

Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction

Gareth William Peters, Ido Nevat, Sai Ganesh Nagarajan, Tomoko Matsui

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Random fields; warped Gaussian Process; Spatial field reconstruction

Online: 11 August 2021 (10:39:35 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0222.v1

Classical and Bayesian Estimation of Two-Parameter Power Function Distribution

Xuechen Liu, Muhammad Arslan, Majid Khan, Syed Masroor Anwar, Zahid Rasheed

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Maximum likelihood estimate; Bayes estimate; Gamma distribution; Squared error loss function; Posterior distribution

Online: 10 August 2021 (09:54:48 CEST)

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Working Paper ARTICLE

Denoising of Spectra by Adaptive Multiwindow Polynomial Fitting

Serguei Charonov

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Denoising; Savitzky-Golay filter; polynomial fitting

Online: 9 August 2021 (09:06:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0178.v1

Detection of Influential Observations in Spatial Regression Model Based on Outliers and Bad Leverage Classification

Ali Mohammed Baba, Habshah Midi, Mohd Bakri Adam, Nur Haizum Bint Abd Rahman

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Spatial regression model; Influential observation; Outlier; Leverage; prediction residual; Masking and swamping; Diagnostic

Online: 9 August 2021 (07:57:56 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202107.0208.v1

Frequency Domain Repercussions of Instantaneous Granger Causality

Luiz Antonio Baccalá, Koichi Sameshima

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: instantaneous Granger causality; total partial directed coherence; information partial directed coherence; total directed transfer function; information directed transfer function; Granger connectivity; Granger influentiability.

Online: 9 July 2021 (09:34:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202106.0416.v1

An Observation on Distribution of Prime Numbers

Dariush Bahrami

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Prime Number; Prime Numbers Distribution; Prime Number Generation; Normal Distribution

Online: 15 June 2021 (15:58:34 CEST)

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Working Paper ARTICLE

Distribution-Based Entropy Weighting Clustering of Skewed and Heavy-Tailed Time Series

Raffaele Mattera, MassimilIano Giacalone, Karina Gibert

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Classification; Generalized Error Distribution; Skewness; Skewed Exponential Power Distribution; Portfolio selection

Online: 28 May 2021 (13:51:14 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202105.0624.v1

Towards Generic Simulation for Demanding Stochastic Processes

Demetris Koutsoyiannis, Panayiotis Dimitriadis

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: stochastics; stochastic processes; stochastic simulation; Monte Carlo simulation; long range de-pendence; persistence; Hurst-Kolmogorov dynamics; climacogram; cumulants; intermittence

Online: 26 May 2021 (08:12:48 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202105.0261.v1

Assessing Point Forecast Bias Across Multiple Time Series: Measures and Visual Tools

Andrey Davydenko, Paul Goodwin

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: forecasting; forecast evaluation; forecast bias; mean bias; median bias; MPE; AvgRel-metrics; AvgRelAME; AvgRelAMdE; RelAME; RelMdE; AvgRelME; AvgRelMdE; OPc

Online: 12 May 2021 (09:48:29 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202105.0107.v1

Base Dependence of Benford Random Variables

Frank Benford

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: significand function; Benford random variables; base b first digit law; Benford spectrum; Benford analysis; see functions; base-invariant significant digits

Online: 6 May 2021 (15:21:24 CEST)

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Preprint TECHNICAL NOTE | doi:10.20944/preprints202001.0045.v3

Event-Based and LHV Simulation of an EPR-B Experiment: EPR-Simple and EPR-Clocked

Richard Gill

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: detection-loophole; coincidence-loophole; Bell experiments; quantum entanglement; event-based simulation; EPR-B experiments

Online: 15 April 2021 (13:37:27 CEST)

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Preprint TECHNICAL NOTE | doi:10.20944/preprints202001.0045.v2

Event-Based and LHV Simulation of an EPR-B Experiment: EPR-Simple and EPR-Clocked

Richard Gill

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: detection-loophole; coincidence-loophole; Bell experiments; quantum entanglement; event-based simulation; EPR-B experiments

Online: 12 April 2021 (12:58:05 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202104.0278.v1

Stochastic Differential Equations in Infinite Dimensional Hilbert Space and its Optimal Control Problem with L´evy Processes

Meijiao Wang, Qiuhong Shi, Qingxin Meng, Maoning Tang

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Stochastic Evolution Equation; Teugels Martingales; Optimal Control; Stochastic Maximum Principle; Verification Theorem

Online: 12 April 2021 (11:21:33 CEST)

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Working Paper ARTICLE

Distribution-Based Entropy Weighting Clustering of Skewed Time Series

Raffaele Mattera, MassimilIano Giacalone, Karina Gibert Oliveiras

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Classification; Generalized Error Distribution; Skewness; Skewed Exponential Power Distribution; Portfolio selection

Online: 7 April 2021 (17:45:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202103.0570.v1

A Stochastic Condensation Mechanism for Inducing Underdispersion in Count Models

Chenangnon Frédéric Tovissodé, Romain Glele Kakai

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Erlang process; condensed distribution; probability generating function; algebraic moments; Poisson remainder distribution; negative binomial remainder distribution

Online: 23 March 2021 (12:57:21 CET)

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Preprint ARTICLE | doi:10.20944/preprints202102.0551.v1

Variational Bayesian Learning and Semiparametric Models on the Double Exponential Family

Hector Zarate-Solano, Edilberto Cepeda-Cuervo

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Variational learning Bayes; semiparametric heterocedastic models; calculus of variations; optimization; biparametric exponential models

Online: 24 February 2021 (15:18:37 CET)

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Preprint ARTICLE | doi:10.20944/preprints202102.0138.v1

Stochastic Behavior of a Two-Unit Parallel System with Dissimilar Units and Optional Vacations under Poisson Shocks

Mohamed S. El-Sherbeny, Zienab M. Hussien

Subject: Computer Science And Mathematics, Probability And Statistics Keywords: Mean time to failure; Poisson shock; Steady-state availability; Steady-state frequency; Supplementary variable technique.

Online: 4 February 2021 (13:07:59 CET)

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Computer Science and Mathematics