The new class of Kummer beta generalized distributions: theory and applications

• Main Author: Pescim, Rodrigo Rossetto
• Publication Date: 2013
• Format: Doctoral thesis
• Language: eng
• Source: Biblioteca Digital de Teses e Dissertações da USP
• Download full: http://www.teses.usp.br/teses/disponiveis/11/11134/tde-30012014-112231/
• topic: Análise Bayesiana; Bayeasian analysis; Birnbaum-Saunders distribution; Distribuição Birnbaum-Saunders; Distribuição gama; Distribuição normal; Gamma distribution; Likelihood ratio; Matriz de informação observada; Normal distribution; Observed information matrix; Razão de verossimilhança

In this study, a new class of generalized distributions was developed, based on the Kummer beta distribution (NG; KOTZ, 1995), which contains as particular cases the exponentiated and beta generators of distributions. The main feature of the new family of distributions is to provide greater flexibility to the extremes of the density function and therefore, it becomes suitable for analyzing data sets with high degree of asymmetry and kurtosis. Also, two new distributions belonging to the new class of distributions, based on the Birnbaum-Saunders and generalized gamma distributions, that has as main characteristic the hazard function which assumes different forms (unimodal, bathtub shape, increase, decrease) were studied. In all studies, general mathematical properties such as ordinary and incomplete moments, generating function, mean deviations, reliability, entropies, order statistics and their moments were discussed. The estimation of parameters is approached by the method of maximum likelihood and Bayesian analysis and the observed information matrix is derived. It is also considered the likelihood ratio statistics and formal goodness-of-fit tests to compare all the proposed distributions with some of its sub-models and non-nested models. The developed results for all studies were applied to six real data sets.