Generalized logistic distribution and its regression model

Abstract

A new generalized asymmetric logistic distribution is defined. In some cases, existing three parameter distributions provide poor fit to heavy tailed data sets. The proposed new distribution consists of only three parameters and is shown to fit a much wider range of heavy left and right tailed data when compared with various existing distributions. The new generalized distribution has logistic, maximum and minimum Gumbel distributions as sub-models. Some properties of the new distribution including mode, skewness, kurtosis, hazard function, and moments are studied. We propose the method of maximum likelihood to estimate the parameters and assess the finite sample size performance of the method. A generalized logistic regression model, based on the new distribution, is presented. Logistic-log-logistic regression, Weibull-extreme value regression and log-Fréchet regression are special cases of the generalized logistic regression model. The model is applied to fit failure time of a new insulation technique and the survival of a heart transplant study.