Discrete Joint Random Variables in Fréchet-Weibull Distribution: A Comprehensive Mathematical Framework with Simulations, Goodness-of-Fit Analysis, and Informed Decision-Making

Diksha Das, Tariq S. Alshammari, Khudhayr A. Rashedi, Bhanita Das, Partha Jyoti Hazarika and Mohamed S. Eliwa ()
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Diksha Das: Department of Statistics, North-Eastern Hill University, Meghalaya 793022, India
Tariq S. Alshammari: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Khudhayr A. Rashedi: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Bhanita Das: Department of Statistics, North-Eastern Hill University, Meghalaya 793022, India
Partha Jyoti Hazarika: Department of Statistics, Dibrugarh University, Assam 786004, India
Mohamed S. Eliwa: Department of Statistics and Operations Research, College of Science, Qassim University, Saudi Arabia

Mathematics, 2024, vol. 12, issue 21, 1-28

Abstract: This paper introduces a novel four-parameter discrete bivariate distribution, termed the bivariate discretized Fréchet–Weibull distribution (BDFWD), with marginals derived from the discretized Fréchet–Weibull distribution. Several statistical and reliability properties are thoroughly examined, including the joint cumulative distribution function, joint probability mass function, joint survival function, bivariate hazard rate function, and bivariate reversed hazard rate function, all presented in straightforward forms. Additionally, properties such as moments and their related concepts, the stress–strength model, total positivity of order 2, positive quadrant dependence, and the median are examined. The BDFWD is capable of modeling asymmetric dispersion data across various forms of hazard rate shapes and kurtosis. Following the introduction of the mathematical and statistical frameworks of the BDFWD, the maximum likelihood estimation approach is employed to estimate the model parameters. A simulation study is also conducted to investigate the behavior of the generated estimators. To demonstrate the capability and flexibility of the BDFWD, three distinct datasets are analyzed from various fields, including football score records, recurrence times to infection for kidney dialysis patients, and student marks from two internal examination statistical papers. The study confirms that the BDFWD outperforms competitive distributions in terms of efficiency across various discrete data applications.

Keywords: bivariate discrete distributions; total positively of order two property; positive quadrant dependent; failure analysis; simulation; data analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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