On the Moments of the Exponentiated Weibull Distribution

Abstract

This article concerns the exponentiated Weibull distribution introduced by Mudholkar et al. (1995). The moments of this distribution have been of some interest, Mudholkar and Hutson (1996) provided a non closed form integral representatior, for the moments while, most recently, Nassar and Eissa (2003) derived a finite sum representation by restricting one of the parameters of the distribution to be c positive integer. In this article, we derive various closed-form representations for the moments with no restrictions imposed on the parameters of the distribution. These representations involve only the (standard) gamma junction and its derivatives.

Key Words:

• Exponentiated Weibull distribution
• Moments