Abstract
A new generalization of the Frechet distribution called Lehmann Type II Frechet Poisson distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, Renyi entropy, stochastic ordering, Bonferroni and Lorenz curve, mean and median deviation, stress-strength parameter are investigated. The maximum likelihood method is used to estimate the model parameters. We examine the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling three real data sets to illustrate empirically its flexibility and tractability in modeling life time data.
Highlights
We examine the performance of the maximum likelihood method by means of a numerical simulation study
Frechet distribution which is known as Inverse Weibull distribution belong to the class of Type II extreme value distribution was developed by Frechet (1924) is a very useful distribution for modeling life time data
The properties of Transmuted Frechet was investigated by Mahmoud and Mandour (2013), Transmuted Exponentiated Frechet was studied by Elbatal et al (2014), Krishna et al (2013) developed and studied Marshall-Olkin Frechet distribution, gamma extended Frechet distribution was studied by Silva et al (2013) and the exponentiated Frechet distribution was studied by Nadarajah and Kotz (2003)
Summary
Frechet distribution which is known as Inverse Weibull distribution belong to the class of Type II extreme value distribution was developed by Frechet (1924) is a very useful distribution for modeling life time data. For more studies on the properties and applications of Frechet distribution, see Kotz and Nadarajah (2000), Harlow (2002). This distribution can be used to analyse life time data that exhibits decreasing increasing or constant failure rate. Models with complex hazard rate shapes such as bathtub, unimodal and other shapes are often encountered in real life time data analysis which may include mortality studies, reliability analysis etc., which the Frechet distribution may not provide a reasonable parametric fit when used for modeling complex phenomenon. The Kumaraswamy Lindley-Poisson distribution which generalises the Lindley-Poisson distribution was studied by Pararai et al (2015), Mohamed and Rezk (2019) developed and studied the properties and applications of the extended Poisson-Frechet distribution. Where γ > 0and ω > 0. γ is a scale parameter and ω is a shape parameter
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