Open Access

ARTICLE

Bivariate Beta–Inverse Weibull Distribution: Theory and Applications

Ali Algarni, Muhammad Qaiser Shahbaz^*

Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

* Corresponding Author: Muhammad Qaiser Shahbaz. Email:

Computer Systems Science and Engineering 2021, 36(1), 83-100. https://doi.org/10.32604/csse.2021.014342

Received 15 September 2020; Accepted 11 November 2020; Issue published 23 December 2020

Abstract

Probability distributions have been in use for modeling of random phenomenon in various areas of life. Generalization of probability distributions has been the area of interest of several authors in the recent years. Several situations arise where joint modeling of two random phenomenon is required. In such cases the bivariate distributions are needed. Development of the bivariate distributions necessitates certain conditions, in a field where few work has been performed. This paper deals with a bivariate beta-inverse Weibull distribution. The marginal and conditional distributions from the proposed distribution have been obtained. Expansions for the joint and conditional density functions for the proposed distribution have been obtained. The properties, including product, marginal and conditional moments, joint moment generating function and joint hazard rate function of the proposed bivariate distribution have been studied. Numerical study for the dependence function has been implemented to see the effect of various parameters on the dependence of variables. Estimation of the parameters of the proposed bivariate distribution has been done by using the maximum likelihood method of estimation. Simulation and real data application of the distribution are presented.

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Keywords

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