Some new distributions and families : theory and applications

Abstract

Several classes of distributions have been introduced in recent decades to extend well-known distributions and provide greater flexibility in modeling real data. Some of these classes are Exponentiated-G, Beta-G, Kumaraswamy-G, Marshall-Olkin-G and Gamma-G. Based on these generators, several new distributions were introduced. In this work, three new families of distributions will be presented: Dual Dagum-G, Exponentiated-Weibull-G and Weibull Flexible- G; and two new probability distributions: Weibull Beta Prime and Weibull extended Weibull. The Weibull Flexible-G family adds only one extra parameter to the baseline distributions, and it includes at least two special cases, namely the Weibull Flexible-Weibull and Weibull Flexible-Gamma distributions, to model bimodal data. Regarding the Weibull Beta Prime distribution, some gains were obtained by modeling bimodal data in addition to modeling data with left skewness. Some properties of the new distributions are presented, and the maximum likelihood method was used to estimate the parameters of the proposed distributions. For the three families, it is shown that their corresponding densities functions can be expressed as linear combinations of exp-G densities. New regression models are also proposed based on the new families and distributions. The potential of the two new distributions and the three families of distributions is Illustrated by simulation studies and applications to real data sets.