<b>A new class of gamma distribution

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, expansions to density and cumulative function, moment generating function, characteristic function, the moments of order , central moments of order , the log likelihood and its partial derivatives and also Rényi entropy, kurtosis, skewness and variance. Some of these properties are indicated 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 data set presented in Choulakian and Stephens (2001) was used. Six models are compared and for the selection of these models was used the Akaike Information Criterion (AIC) and tests of Cramer-Von Mises and Anderson-Darling to assess the models fit. Lastly, the conclusions from the analysis and comparison of the results obtained are presented, as well as the directions for future researches.