A novel method to generating two-sided class of probability distributions

Abstract

We define a new two-sided class F of distributions and a generalized class by compounding this class with a baseline distribution G. The new model is called the general two-sided FG class. Some of its properties are provided. The proposed model is specialized taking the Weibull and exponential for F and G, respectively. For a new specialized distribution, we obtain the survival, quantiles and hazard rate. We estimate the parameters by maximum likelihood, Bayesian and parametric and non-parametric bootstrap methods. We conduct a simulation study to check the accuracy of the estimators. The classic and Bayesian approaches are illustrated by means of a real data set. We show that the proposed model fits better than the generalized two-sided exponential and generalized transmuted two-sided exponential distributions.