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Properties and methods of estimation for a bivariate exponentiated Fréchet distribution

In: Mathematica Slovaca, vol. 70, no. 5
Abdus Saboor - Hassan S. Bakouch - Fernando A. Moala - Sheraz Hussain
Detaily:
Rok, strany: 2020, 1211 - 1230
Kľúčové slová:
Copula, exponentiated Fr´echet distribution, maximum likelihood estimators, Fisher information matrix, Bayesian inference, least squares method
O článku:
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.
Ako citovať:
ISO 690:
Saboor, A., Bakouch, H., Moala, F., Hussain, S. 2020. Properties and methods of estimation for a bivariate exponentiated Fréchet distribution. In Mathematica Slovaca, vol. 70, no.5, pp. 1211-1230. 0139-9918. DOI: https://doi.org/DOI: 10.1515/ms-2017-0426

APA:
Saboor, A., Bakouch, H., Moala, F., Hussain, S. (2020). Properties and methods of estimation for a bivariate exponentiated Fréchet distribution. Mathematica Slovaca, 70(5), 1211-1230. 0139-9918. DOI: https://doi.org/DOI: 10.1515/ms-2017-0426
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 27. 9. 2020