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.

中文翻译：

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二元指数 Fréchet 分布的性质和估计方法

摘要 本文介绍了指数Fréchet 分布的二元扩展，即边缘为单变量指数Fréchet 分布的二元指数Fréchet (BvEF) 分布。讨论了所提出的分布的几个属性，例如联合生存函数、联合概率密度函数、边际概率密度函数、条件概率密度函数、矩、边际和二元矩生成函数。此外，建议的分布是通过 Marshall-Olkin 生存联结获得的。通过观察信息矩阵的最大似然来研究参数的估计。除了最大似然估计方法，我们考虑贝叶斯推理和最小二乘估计，并比较 BvEF 的这三种方法。进行模拟研究以通过所提出的估计方法来比较估计器的性能。建议的双变量分布与其他相关的双变量分布被拟合到现实生活中的配对数据集。结果表明，BvEF 分布在使用多项拟合优度检验的比较分布中具有优越的性能。