On the Four-Parameter T-extended Standard U-quadratic Exponentiated Weibull Distribution

Abstract

This paper identifies the characteristics of a three-parameter distribution which is an extension of the Exponentiated Weibull distribution (ExW) introduced by Pal, et al. in 2006 [18] and Mudholkar and Srivastava in 1993 [15]. This extended distribution is labeled as T-extended Standard U-quadratic Exponentiated Weibull distribution (TeSU-ExW). The proposed distribution uses the properties of the U-quadratic distribution and the Transformed Transformer family of distributions in its derivation. Let X be a random variable that follows an ExW distribution with scale parameter λ and shape parameters β and γ. This study derives the cumulative distribution function (cdf) and the corresponding probability density function (pdf) of TeSU-ExW. Moreover, properties such as its moment, moment generating function, mean, median, mode and variance are also obtained in this paper.