Bivariate Epanechnikov-Weibull distribution based on Sarmanov copula: properties, simulation, and uncertainty measures with applications

G. M. Mansour; M. A. Abd Elgawad; A. S. Al-Moisheer; H. M. Barakat; M. A. Alawady; I. A. Husseiny; M. O. Mohamed; G. M. Mansour; M. A. Abd Elgawad; A. S. Al-Moisheer; H. M. Barakat; M. A. Alawady; I. A. Husseiny; M. O. Mohamed

doi:10.3934/math.2025572

AIMS Mathematics

2025, Volume 10, Issue 5: 12689-12725. doi: 10.3934/math.2025572

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Bivariate Epanechnikov-Weibull distribution based on Sarmanov copula: properties, simulation, and uncertainty measures with applications

1.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
2.
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia

Received: 28 February 2025 Revised: 16 April 2025 Accepted: 16 May 2025 Published: 30 May 2025
MSC : 60B12, 62G30

The modeling of bivariate data in statistics often requires constructing families of bivariate distributions with predefined marginals. In this study, we introduced a novel bivariate distribution, denoted as EP-WD-SAR, which combines the Sarmanov (SAR) copula with the Epanechnikov-Weibull marginal distribution (EP-WD). We analyzed its statistical properties, including product moments, correlation coefficient, moment-generating function, conditional distribution, and concomitants of order statistics. Additionally, we evaluated key reliability and information measures such as the hazard function, reversed hazard function, bivariate extropy, bivariate weighted extropy, and bivariate cumulative residual extropy. Parameter estimation was performed using maximum likelihood, asymptotic confidence intervals, and Bayesian methods. Finally, we demonstrated the advantages of the EP-WD-SAR model over existing alternatives, including the bivariate Weibull-SAR, bivariate Epanechnikov-exponential-SAR, bivariate exponential-SAR, and bivariate Chen-SAR distributions through applications to real data sets.
- Sarmanov family,
- Epanechnikov-Weibull distribution,
- maximum likelihood estimation,
- Bayesian estimation,
- confidence intervals,
- bootstrap,
- simulation
Citation: G. M. Mansour, M. A. Abd Elgawad, A. S. Al-Moisheer, H. M. Barakat, M. A. Alawady, I. A. Husseiny, M. O. Mohamed. Bivariate Epanechnikov-Weibull distribution based on Sarmanov copula: properties, simulation, and uncertainty measures with applications[J]. AIMS Mathematics, 2025, 10(5): 12689-12725. doi: 10.3934/math.2025572

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Abstract

The modeling of bivariate data in statistics often requires constructing families of bivariate distributions with predefined marginals. In this study, we introduced a novel bivariate distribution, denoted as EP-WD-SAR, which combines the Sarmanov (SAR) copula with the Epanechnikov-Weibull marginal distribution (EP-WD). We analyzed its statistical properties, including product moments, correlation coefficient, moment-generating function, conditional distribution, and concomitants of order statistics. Additionally, we evaluated key reliability and information measures such as the hazard function, reversed hazard function, bivariate extropy, bivariate weighted extropy, and bivariate cumulative residual extropy. Parameter estimation was performed using maximum likelihood, asymptotic confidence intervals, and Bayesian methods. Finally, we demonstrated the advantages of the EP-WD-SAR model over existing alternatives, including the bivariate Weibull-SAR, bivariate Epanechnikov-exponential-SAR, bivariate exponential-SAR, and bivariate Chen-SAR distributions through applications to real data sets.

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