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On Six-Parameter Fréchet Distribution: Properties and Applications

Author(s)
Haitham M. Yousof Department of Statistics, Mathematics and Insurance Benha University, Egypt
Ahmed Z. Afify Department of Statistics, Mathematics and Insurance Benha University, Egypt
Abd El Hadi N. Ebraheim Institute of Statistical Studies & Research Cairo University, Egypt.
G. G. Hamedani Department of Mathematics, Statistics and Computer Science Marquette University, USA
Nadeem Shafique Butt Department of Family and Community Medicine, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia
Abstract
This paper introduces a new generalization of the transmuted Marshall-Olkin Fréchet distribution of Afify et al. (2015), using Kumaraswamy generalized family. The new model is referred to as Kumaraswamy transmuted Marshall-Olkin Fréchet distribution. This model contains sixty two sub-models as special cases such as the Kumaraswamy transmuted Fréchet, 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 Rényi 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. 
Publication Details
Page(s) 281-299
DOI DOI not available
Published Journal: Pakistan Journal of Statistics and Operation Research, Volume: 12, Issue: 2, Year: 2016

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Keywords
maximum likelihood estimation, Order Statistics, Goodness-of-fit, Moments of residual life
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