A Study of the Logistic Exponentiated-Exponential Distribution and Its Applications

Abstract

The logistic-X (LX) family of distributions based on the logistic random variable was formulated recently by Tahir et al. [1]. We study a new special model of this family called the logistic exponentiated-exponential (LEE) distribution. Its density function can be symmetric, left-skewed, right-skewed, and reversed-J shaped, and its hazard rate can be decreasing and upside-down bathtub shapes. We provide a useful power series for its quantile function and a mixture representation for its density function. The parameters of the LEE model are estimated by maximum likelihood. Three Ozone data sets are modeled to illustrate the applicability of the new model.