A New Class of Bivariate Distributions: Properties, Estimation, and Modeling

Jumanah Ahmed Darwish, Saman Hanif Shahbaz and Muhammad Qaiser Shahbaz ()
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Jumanah Ahmed Darwish: Department of Mathematics and Statistics, University of Jeddah, Jeddah 21959, Saudi Arabia
Saman Hanif Shahbaz: Department of Statistics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Muhammad Qaiser Shahbaz: Department of Statistics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2024, vol. 12, issue 24, 1-33

Abstract: The development of bivariate distributions is a challenging area of research, and a novel class of bivariate distributions is proposed in this paper. Certain useful mathematical characteristics of the proposed class of bivariate distributions are explored in general. These properties include the joint and conditional and joint survival function moments and measures of dependence. The parameters of the proposed class of distributions are estimated using the maximum likelihood method of estimation. A multivariate version of the proposed class is also proposed, and some necessary properties are discussed. The multivariate dependence measures are obtained for the proposed multivariate class of distributions. A new bivariate power function distribution is proposed using the power function distribution as a baseline distribution in the proposed bivariate class. Some useful properties of the proposed bivariate distribution are studied. The parameters of the proposed bivariate distribution are estimated using the maximum likelihood method. An extensive simulation study has been conducted to see the performance of the estimation method. The new bivariate power function distribution is used to model some real data.

Keywords: class of distributions; bivariate distributions; dependence measures; reliability analysis; maximum likelihood estimation; power function distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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