On bivariate compound exponentiated survival function of the beta distribution: estimation and prediction

Abstract

A bivariate distribution is a probability distribution that describes the joint behavior of two random variables. It provides information about the simultaneous variation of two variables, allowing us to analyze their relationship and dependencies. This article discussed the bivariate compound exponentiated survival function of the beta distribution. the joint cumulative distribution function and the joint probability density function were found in closed forms. Several characteristics of this distribution have been discussed. The maximum likelihood (ML) estimators of the parameters and two sample ML predictions of the future observations are derived. The Bayes estimators (BEs) of the parameters based on the squared error loss function and two sample Bayesian predictions of the future observations are presented. The performance of the proposed bivariate distributions is examined using a simulation study. Finally, two data sets are considered in the framework of the proposed distributions to demonstrate their flexibility for real-life applications.