Abstract
The exponentiated gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called the beta exponentiated gamma (BEG) distribution has been introduced. The new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the BEG distribution has been provided. We derived the rth moment and moment generating function for this distribution. Moreover, we discussed the maximum likelihood estimation of this distribution under a simulation study.
Highlights
Gamma distributions are some of the most popular models for hydrological processes
The exponentiated gamma (EG) distribution has been introduced by Gupta et al (1998), which has cumulative distribution function (CDF) and a probability density function of the form, respectively; G(x, )
The order statistics from exponentiated gamma distribution and associated inference was discussed by Shawky and Bakoban (2009)
Summary
Gamma distributions are some of the most popular models for hydrological processes. One of the important families of distributions in lifetime tests is the exponentiated gamma (EG) distribution. Singh et al (2011) proposed Bayes estimators of the parameter of the exponentiated gamma distribution and associated reliability function under general entropy loss function for a censored sample. (2011) proposed Bayes estimators of the parameter of the exponentiated gamma distribution and associated reliability function under general entropy loss function for a censored sample. Many authors considered various forms of G and studied their properties: Nadarajah and Kotz (2004) introduced the beta Gumbel (BGu) distribution by taking G(x) to be the CDF of the Gumbel distribution and provided closed form expressions for the moments, the asymptotic distribution of the extreme order statistics and discussed the maximum likelihood estimation procedure. The properties of F(x) for any beta G distribution defined from a parent G(x) in Equation [3] could, in principle, follow from the properties of the hyper geometric function which are well established in the literature; see, for example, Section 9.1 of Gradshteyn and Ryzhik (2000). The discussion and conclusion regarding the study have been presented in the section 7
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