A New Class of Gamma distribution

TL;DR

This paper introduces a new class of gamma-based probability distributions, explores their statistical properties, and demonstrates their application to real data with model selection criteria.

Contribution

It proposes a novel class of distributions derived from gamma, detailing their properties and applying them to real data for model comparison.

Findings

The new distribution class has well-defined statistical properties.

Application to real data shows competitive model fit.

Model selection criteria favor the proposed class in the example.

Abstract

This paper presents a new class of probability distributions generated from the gamma distribution. For the new class proposed, we present several statistical properties, such as the risk function, the density expansions, Moment-generating function, characteristic function, the moments of order m, central moments of order m, the log likelihood and its partial derivatives and also entropy, kurtosis, symmetry and variance. These same properties are determined for a particular distribution within this new class that is used to illustrate the capability of the proposed new class through an application to a real data set. The database presented in Choulakian and Stephens (2001) was used. Six models are compared and for the selection of these models were used the Akaike Information Criterion (AIC), the Akaike Information Criterion corrected (AICc), Bayesian Information Criterion (BIC), Hannan Quinn Information Criterion (HQIC) and tests of Cramer-Von Mises and Anderson-Darling to assess the models fit. Finally, we present the conclusions from the analysis and comparison of the results obtained and the directions for future work.