Bivariate Epanechnikov-exponential distribution: statistical properties, reliability measures, and applications to computer science data

H. M. Barakat; M. A. Alawady; I. A. Husseiny; M. Nagy; A. H. Mansi; M. O. Mohamed; H. M. Barakat; M. A. Alawady; I. A. Husseiny; M. Nagy; A. H. Mansi; M. O. Mohamed

doi:10.3934/math.20241550

AIMS Mathematics

2024, Volume 9, Issue 11: 32299-32327. doi: 10.3934/math.20241550

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Bivariate Epanechnikov-exponential distribution: statistical properties, reliability measures, and applications to computer science data

1.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
2.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O.Box 2455, Riyadh 11451, Saudi Arabia
3.
DICA, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, MI, Italy

Received: 30 July 2024 Revised: 05 November 2024 Accepted: 11 November 2024 Published: 15 November 2024
MSC : 60B12, 62G30

One important area of statistical theory and its applications to bivariate data modeling is the construction of families of bivariate distributions with specified marginals. This motivates the proposal of a bivariate distribution employing the Farlie-Gumbel-Morgenstern (FGM) copula and Epanechnikov exponential (EP-EX) marginal distribution, denoted by EP-EX-FGM. The EP-EX distribution is a complementing distribution, not a rival, to the exponential (EX) distribution. Its simple function shape and dependence on a single scale parameter make it an ideal choice for marginals in the suggested new bivariate distribution. The statistical properties of the EP-EX-FGM model are examined, including product moments, coefficient of correlation between the internal variables, moment generating function, conditional distribution, concomitants of order statistics (OSs), mean residual life function, and vitality function. In addition, we calculated reliability and information measures including the hazard function, reversed hazard function, positive quadrant dependence feature, bivariate extropy, bivariate weighted extropy, and bivariate cumulative residual extropy. Estimating model parameters is accomplished by utilizing maximum likelihood, asymptotic confidence intervals, and Bayesian approaches. Finally, the advantage of EP-EX-FGM over the bivariate Weibull FGM distribution, bivariate EX-FGM distribution, and bivariate generalized EX-FGM distribution is illustrated using actual data sets.
- FGM copula,
- Epanechnikov-exponential distribution,
- maximum likelihood estimation,
- Bayesian estimation,
- confidence intervals
Citation: H. M. Barakat, M. A. Alawady, I. A. Husseiny, M. Nagy, A. H. Mansi, M. O. Mohamed. Bivariate Epanechnikov-exponential distribution: statistical properties, reliability measures, and applications to computer science data[J]. AIMS Mathematics, 2024, 9(11): 32299-32327. doi: 10.3934/math.20241550

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Abstract

One important area of statistical theory and its applications to bivariate data modeling is the construction of families of bivariate distributions with specified marginals. This motivates the proposal of a bivariate distribution employing the Farlie-Gumbel-Morgenstern (FGM) copula and Epanechnikov exponential (EP-EX) marginal distribution, denoted by EP-EX-FGM. The EP-EX distribution is a complementing distribution, not a rival, to the exponential (EX) distribution. Its simple function shape and dependence on a single scale parameter make it an ideal choice for marginals in the suggested new bivariate distribution. The statistical properties of the EP-EX-FGM model are examined, including product moments, coefficient of correlation between the internal variables, moment generating function, conditional distribution, concomitants of order statistics (OSs), mean residual life function, and vitality function. In addition, we calculated reliability and information measures including the hazard function, reversed hazard function, positive quadrant dependence feature, bivariate extropy, bivariate weighted extropy, and bivariate cumulative residual extropy. Estimating model parameters is accomplished by utilizing maximum likelihood, asymptotic confidence intervals, and Bayesian approaches. Finally, the advantage of EP-EX-FGM over the bivariate Weibull FGM distribution, bivariate EX-FGM distribution, and bivariate generalized EX-FGM distribution is illustrated using actual data sets.

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