Bivariate Burr Type III Distribution: Estimation and Prediction

Abstract

In this paper, a bivariate Burr Type III distribution is constructed and some of its statistical properties such as bivariate probability density function and its marginal, joint cumulative distribution and its marginal, reliability and hazard rate functions are studied. The joint probability density function and the joint cumulative distribution are given in closed forms. The joint expectation of this distribution is proposed. The maximum likelihood estimation and prediction for a future observation are derived. Also, Bayesian estimation and prediction are considered under squared error loss function. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, a data set is analyzed under the proposed distribution to illustrate its flexibility for real-life application.

A Study on Bivariate Burr Tybe Iii Distribution

“…In the statistical literature, several methodologies of constructing bivariate and multivariate distributions based on marginal and conditional distributions were proposed by Kotz et al (2000), Arnold et al (1999;2001), Balakrishnan and Lai (2009), Mahmoud et al(2021) and among others. Domma (2009) extended some results related to the dependence structure of the bivariate Burr Type III distribution; proposed by Rodriguez (1980) using copula representations of bivariate distributions.…”