The exponentiated gamma distribution with application to drought data. (English) Zbl 1155.33305

Summary: Gamma distributions are some of the most popular models for hydrological processes. In this paper, a very flexible family which contains the gamma distribution as a particular case is introduced. This distribution generalizes the standard gamma distribution in the same way the exponentiated exponential distribution [R. D. Gupta et al., Biom. J. 43, 117–130 (2001; Zbl 0997.62076); D. Roy, Calcutta Stat. Assoc. Bull. 48, No. 191–192, 169–177 (1998; Zbl 0927.62010)] generalizes the standard exponential distribution. We refer to this new distribution as the exponentiated gamma distribution. A comprehensive treatment of the mathematical 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 \(n\)-th 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.


33C90 Applications of hypergeometric functions
62E99 Statistical distribution theory
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