Properties and methods of estimation for a bivariate exponentiated Fr´ echet distribution Abdus Saboor a,* , Hassan S. Bakouch b , Fernando A. Moala c , Sheraz Hussain a a Institute of Numerical Sciences, Kohat University of Science & Technology, Kohat, 26000, Pakistan b Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt c Department of Statistics, State University of Sao Paulo, Brazil Abstract In this paper, a bivariate extension of exponentiated Fr´ echet distribution is introduced, namely a bivariate exponentiated Fr´ echet (BvEF) distribution whose marginals are univariate exponentiated Fr´ echet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probabil- ity 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 simu- lation 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. Keywords: Copula, exponentiated Fr´ echet distribution, Maximum likelihood estimators, Fisher information matrix, Bayesian inference, Least squares method. ✩ Corresponding author Email address: saboorhangu@gmail.com (Abdus Saboor) Preprint submitted to Mathematica Slovaca January 3, 2020