Abstract
A new extension of the generalized gamma distribution with six parameter called the Kummer beta generalized gamma distribution is introduced and studied. It contains at least 28 special models such as the beta generalized gamma, beta Weibull, beta exponential, generalized gamma, Weibull and gamma distributions and thus could be a better model for analyzing positive skewed data. The new density function can be expressed as a linear combination of generalized gamma densities. Various mathematical properties of the new distribution including explicit expressions for the ordinary and incomplete moments, generating function, mean deviations, entropy, density function of the order statistics and their moments are derived. The elements of the observed information matrix are provided. We discuss the method of maximum likelihood and a Bayesian approach to fit the model parameters. The superiority of the new model is illustrated by means of three real data sets.
Highlights
The generalized gamma (GG) distribution (Stacy, 1962) is an important lifetime model since it includes as special models the exponential, Weibull, gamma and Rayleigh distributions, among others
In this paper we study a new six-parameter model called the Kummer beta generalized gamma (KBGG) distribution which contains at least 28 special models
For k =1, the KBGG distribution reduces to the Kummer beta Weibull (KBW) distribution
Summary
The generalized gamma (GG) distribution (Stacy, 1962) is an important lifetime model since it includes as special models the exponential, Weibull, gamma and Rayleigh distributions, among others. For an arbitrary baseline distribution G(x;γ) with parameter vector γ and density function g(x;γ) Pescim et al (2012) proposed the Kummer beta generalized (denoted by the prefix "KB-G" for short) cumulative function defned by. In this paper we study a new six-parameter model called the Kummer beta generalized gamma (KBGG) distribution which contains at least 28 special models. We denote by X a random variable following (5), say X ∼ KBGG(a, b, c, α, β, k) This density has five shape parameters a, b, c, β and k which allow for a high degree of flexibility.
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