On Six-Parameter Frechet Distribution: Properties and Applications

Haitham M. Yousof, Ahmed Z A…fify, Abd El Hadi N Ebraheim, G G Hamedani, Nadeem Shafique Butt

Abstract


This paper introduces a new generalization of the transmuted Marshall-Olkin Frechet distribution of Afy et al. (2015), using Kumaraswamy generalized family. The new model is referred to as Kumaraswamy transmuted Marshall-Olkin FrØchet distribution. This model contains sixty two sub-models as special cases such as the Kumaraswamy transmuted Frechet, Kumaraswamy transmuted Marshall-Olkin, generalized inverse Weibull and Kumaraswamy Gumbel type II distributions, among others. Various mathematical properties of the proposed distribution including closed forms for ordinary and incomplete moments, quantile and generating functions and Renyi and -entropies are derived. The unknown parameters of the new distribution are estimated using the maximum likelihood estimation. We illustrate the importance of the new model by means of two applications to real data sets.

Keywords


Moments of residual life, Goodness-of-…t, Order Statistics, Maximum Likelihood Estimation.

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DOI: http://dx.doi.org/10.18187/pjsor.v12i2.1327

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Title

On Six-Parameter Frechet Distribution: Properties and Applications

Keywords

Moments of residual life, Goodness-of-…t, Order Statistics, Maximum Likelihood Estimation.

Description

This paper introduces a new generalization of the transmuted Marshall-Olkin Frechet distribution of A…fy et al. (2015), using Kumaraswamy generalized family. The new model is referred to as Kumaraswamy transmuted Marshall-Olkin FrØchet distribution. This model contains sixty two sub-models as special cases such as the Kumaraswamy transmuted Frechet, Kumaraswamy transmuted Marshall-Olkin, generalized inverse Weibull and Kumaraswamy Gumbel type II distributions, among others. Various mathematical properties of the proposed distribution including closed forms for ordinary and incomplete moments, quantile and generating functions and Renyi and -entropies are derived. The unknown parameters of the new distribution are estimated using the maximum likelihood estimation. We illustrate the importance of the new model by means of two applications to real data sets.

Date

2016-06-03

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 12 No. 2, 2016



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810