The Exponentiated Gamma Distribution with Application to Drought Data

Abstract

Gamma distributions are some of the most popular models for hydrological processes. In this paper, a very flexible family which contains the gamma distrihution as a particular case is introduced. This distribution generalizes the standard gamma distribution in the same way the exponentiated exponential distribution (Gupta et al., 1998; Roy, 1998) generalizes the standard exponential distribution. We refer to this new distribution as the exponentiated gamma distribution. A comprehensive treatment of the math­ ematical properties is provided by deriving expressions for various particular cases and bounds, analytical shapes of the corresponding probability density function and the hazard rate function, moment generating function, the nth moment, skewness, kurtosis, mean deviation , Shannon entropy, and the asymptotic distribution of the extreme order statistics. Estimation procedure by the method of maximum likelihood and an expression for the Fisher information matrix are also provided. Finally, an application to drought data from the State of Nebraska is illustrated.