Some extensions of the Chen distribution and the proposal of two new distribution families : a study focused on simulations, regression and applications

Abstract

In recent years, several new distributions have appeared in the literature. These new distributions are introduced by adding extra parameters to the baseline distributions, from distribution generators. The more known generators are, Beta-G, Kumasrawamy- G, Marshall-Olkin-G, odd-log-logistic-G. Numerous new distributions using these various generators have been introduced. In this work, three others new distributions and two other new families of distributions are proposed. The three new distributions introduced, these were obtained from the bi-parametric Chen distribution, which has a bathtub-shaped failure rate function. The Chen distribution was inserted in the generators gamma-G, Mcdonald-G and logistic-X, thus giving names to gamma-Chen, Mcdonald-Chen and logistic-Chen distributions. The parameters of these distributions are estimated by the maximum likelihood method. Simulation studies and applications to real data are considered to show the potentiality of the three new distributions and the two families of distributions. In the losgistic-Chen distribution, a regression model for censored data, having reparameterization at the median, is also introduced. The two families of distributions proposed are: the Stacy-G, which is introduced from the Stacy distribution and the unit gamma-G, based on the unit gamma distribution. These two families of distributions add two extra parameters to the baseline distributions. The Stacy-G family also has the gamma-G family as a special case. In both families it is shown that their respective densities functions can be written as a linear combination of exp-G densities. Taking the log of a non-negative random variable from the baseline distribution, and reparameterizing for the location-scale family, the regression model for these two classes of distributions are introduced.