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2017•Unpublished venueRequires access

Gamma Distribution

Myke King

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Abstract

This chapter describes the range of possible modifications in gamma distribution. These are inverse gamma distribution/Pearson-V distribution, log-gamma distribution, generalised gamma distribution/transformed gamma distribution/Stacy-Mihram distribution, and q-gamma distribution. There are at least five distributions that are described as the log-gamma distribution. The chapter also describes all these. The generalised gamma distribution includes the gamma, Weibull-II and exponential distributions as special cases, but these are also covered by the Amoroso distribution. The chapter shows the effect of varying shape parameters (δ1 and δ2). It further shows the effect of varying δ, with a fixed at 0 and β at 1. The addition of a shape parameter will usually mean that the q-gamma distribution will be a better fit than the gamma distribution.

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What this paper is about

This chapter describes the range of possible modifications in gamma distribution. These are inverse gamma distribution/Pearson-V distribution, log-gamma distribution, generalised gamma distribution/transformed gamma distribution/Stacy-Mihram distribution, and q-gamma distribution. There are at least five distributions that are described as the log-gamma distribution. The chapter also describes all these. The generalised gamma distribution includes the gamma, Weibull-II and exponential distributions as special cases, but these are also covered by the Amoroso distribution. The chapter shows the effect of varying shape parameters (δ1 and δ2). It further shows the effect of varying δ, with a fixed at 0 and β at 1. The addition of a shape parameter will usually mean that the q-gamma distribution will be a better fit than the gamma distribution.

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Available abstract

This chapter describes the range of possible modifications in gamma distribution. These are inverse gamma distribution/Pearson-V distribution, log-gamma distribution, generalised gamma distribution/transformed gamma distribution/Stacy-Mihram distribution, and q-gamma distribution. There are at least five distributions that are described as the log-gamma distribution. The chapter also describes all these. The generalised gamma distribution includes the gamma, Weibull-II and exponential distributions as special cases, but these are also covered by the Amoroso distribution. The chapter shows the effect of varying shape parameters (δ1 and δ2). It further shows the effect of varying δ, with a fixed at 0 and β at 1. The addition of a shape parameter will usually mean that the q-gamma distribution will be a better fit than the gamma distribution.

Key concepts: Gamma distribution, Generalized gamma distribution, Inverse-gamma distribution, Generalized integer gamma distribution, Distribution (mathematics), Variance-gamma distribution, Ratio distribution, Weibull distribution

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