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Three-Parameter Generalized Gamma Distribution

Vijay P. Singh, Lan Zhang

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Abstract

The three-parameter generalized gamma (TPGG) distribution is a generalization of the two-parameter gamma distribution and includes as special cases the exponential distribution, the two-parameter gamma distribution, the Weibull distribution, and the lognormal distribution that are employed for frequency analysis in water engineering. In this chapter, the TPGG distribution is derived using the entropy theory and then its parameters are estimated with the principle of maximum entropy and the methods of maximum likelihood estimation and moments.

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What this paper is about

The three-parameter generalized gamma (TPGG) distribution is a generalization of the two-parameter gamma distribution and includes as special cases the exponential distribution, the two-parameter gamma distribution, the Weibull distribution, and the lognormal distribution that are employed for frequency analysis in water engineering. In this chapter, the TPGG distribution is derived using the entropy theory and then its parameters are estimated with the principle of maximum entropy and the methods of maximum likelihood estimation and moments.

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Available abstract

The three-parameter generalized gamma (TPGG) distribution is a generalization of the two-parameter gamma distribution and includes as special cases the exponential distribution, the two-parameter gamma distribution, the Weibull distribution, and the lognormal distribution that are employed for frequency analysis in water engineering. In this chapter, the TPGG distribution is derived using the entropy theory and then its parameters are estimated with the principle of maximum entropy and the methods of maximum likelihood estimation and moments.

Key concepts: Gamma distribution, Generalized integer gamma distribution, Generalized gamma distribution, Generalized beta distribution, Weibull distribution, Distribution fitting, Log-Cauchy distribution, Mathematics

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