Properties and methods of estimation for a bivariate exponentiated Fréchet distribution

Abstract

In this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional probability density function, moments, marginal and bivariate moment generating functions. Moreover, the proposed distribution is obtained by the Marshall-Olkin survival copula. Estimation of the parameters is investigated by the maximum likelihood with the observed information matrix. In addition to the maximum likelihood estimation method, we consider the Bayesian inference and least square estimation and compare these three methodologies for the BvEF. A simulation study is carried out to compare the performance of the estimators by the presented estimation methods. The proposed bivariate distribution with other related bivariate distributions are fitted to a real-life paired data set. It is shown that, the BvEF distribution has a superior performance among the compared distributions using several tests of goodness–of–fit.

Mixture Model on Development of Bivariate Product Distribution and its Properties

“…Studying through the literature, Marshal Olkin survival copula method as predominantly used in the development of bivariate Dagum distribution, Muhammed [18], bivariate Lindley distributions based on stress and shock models, Oliveira [19], bivariate exponentiated Frétchet distribution, Saboor [20], Marshall-Olkin bivariate Weibull distribution, Kundu [21], bivariate generalized exponential, Kundu [22] etc, like many other methods, follow dependent structure or measurement. In other words, the random variables are correlated; and this area has been exhaustively developed using identical (same) distribution in their bivariate development.…”