Staff Members - Benha University
On Six-Parameter Fréchet Distribution: Properties and Applications
• 2016
Publication Information
Authors
Haitham M. Yousof
Department of Statistics, Mathematics and Insurance
Benha University, Egypt
haitham.yousof@fcom.bu.edu.eg
Ahmed Z. Afify
Department of Statistics, Mathematics and Insurance
Benha University, Egypt
Ahmed.afify@fcom.bu.edu.eg
Abd E
Keywords
Moments of residual life, Goodness-of-fit, Order Statistics, Maximum
Likelihood Estimation.
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publication.type
International
Paper Link
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Supplementary Materials
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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.
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.