PROPERTIES AND METHODS OF ESTIMATION FOR A BIVARIATE EXPONENTIATED FRECHET DISTRIBUTION - Saboor, Abdus; Bakouch, Hassan S.; Moala, Fernando A. [UNESP]; Hussain, Sheraz (Walter De Gruyter Gmbh, 2020)
In this paper, a bivariate extension of exponentiated Frechet distribution is introduced, namely a bivariate exponentiated Frechet (BvEF) distribution whose marginals are univariate exponentiated Frechet 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. (C) 2020 Mathematical Institute Slovak Academy of Sciences
Keywords: Copula; exponentiated Frechet distribution; maximum likelihood estimators; Fisher information matrix; Bayesian inference; least squares method