Abstract
Abstract: In this paper, a new class of five parameter gamma-exponentiated or generalized modified Weibull (GEMW) distribution which includes exponential, Rayleigh, Weibull, modified Weibull, exponentiated Weibull, exponentiated exponential, exponentiated modified Weibull, exponentiated modified exponential, gamma-exponentiated exponential, gamma exponentiated Rayleigh, gamma-modified Weibull, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh and gamma-exponential distributions as special cases is proposed and studied. Mathematical properties of this new class of distributions including moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to real data sets presented in order to illustrate the usefulness of this new class of distributions and its sub-models.
Highlights
Weibull distribution (Weibull, 1951) has exponential and Rayleigh as special sub-models and it is one of the most popular distributions for modeling lifetime data with monotone failure rates
For a review of these models, the reader can refer to Pham and Lai (2007), where the authors summarized some generalizations of Weibull distribution
Jones (2004) studied a family of distributions derived from the distribution of order statistics, the beta-generated family proposed by Eugene et al (2002)
Summary
Weibull distribution (Weibull, 1951) has exponential and Rayleigh as special sub-models and it is one of the most popular distributions for modeling lifetime data with monotone failure rates. In this paper we introduce a new distribution with ve pa-rameters, referred to as the gammaexponentiated modi ed Weibull (GEMW) distribution with the aim of attracting wider application in reliability, biology and other areas of research This generalization contains as special sub-models several distributions such as the EW (Gupta and Kundu, 1999), MW, generalized Rayleigh (GR) (Kundu and Rekab, 2005) and a new sub-model, namely Gamma modi ed Weibull (GMW) distributions, along with several others. The GEMW distribution is useful for modeling bathtub-shaped failure rate data and suitable for testing goodness-of- t of some special sub-models such as the EW (Gupta and Kundu, 1999), MW, GMW (new) and GEW distributions.
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