Abstract
The generalized gamma distribution is a continuous probability distribution with three parameters. It is a generalization of the two-parameter gamma distribution. Since many distributions commonly used for parametric models in survival analysis (such as the Exponential distribution , the Weibull distribution and the Gamma distribution) are special cases of the generalized gamma, it is sometimes used to determine which parametric model is appropriate for a given set of data. Generalized gamma distribution is one of the distributions used in frailty modeling. In this study , it is shown that generalized gamma distribution has three sub-families and its application to the analysis of a survival data has also been explored. The parametric modeling approach has been carried out to find the expected results.
Highlights
The early generalization of gamma distribution can be traced back to Amoroso(1925)who discussed a generalized gamma distribution and applied it to fit income rates
Since many distributions commonly used for parametric models in survival analysis are special cases of the generalized gamma, it is sometimes used to determine which parametric model is appropriate for a given set of data
Johnson et al gave a four parameter generalized gamma distribution which reduces to the generalized gamma distribution defined by Stacy (1962) when the location parameter is set to zero.The generalized gamma defined by Stacy (1962) is a three-parameter exponentiated gamma distribution
Summary
The early generalization of gamma distribution can be traced back to Amoroso(1925)who discussed a generalized gamma distribution and applied it to fit income rates. Johnson et al gave a four parameter generalized gamma distribution which reduces to the generalized gamma distribution defined by Stacy (1962) when the location parameter is set to zero.The generalized gamma defined by Stacy (1962) is a three-parameter exponentiated gamma distribution. Mudholkar and Srivastava (1993) introduced the exponentiated method to derive a distribution. Agarwal and Al-Saleh (2001) applied generalized gamma to study hazard rates. Balakrishnan and Peng (2006) applied this distribution to develop generalized gamma frailty model.Nadarajah and Gupta (2007) proposed another type of generalized gamma distribution with application to fitting drought data. Cordeiro et al (2012) derived another generalization of Stacy’s generalized gamma distribution using exponentiated method, and applied it to life time and survival analysis
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