THE EXPONENTIATED FRECHET DISTRIBUTION

by Saralees Nadarajah and Samuel Kotz.

Abstract: Gupta et al. [Communication in Statistics---Theory and Methods, 1998, 27, 887--904] introduced the exponentiated exponential distribution as a generalization of the standard exponential distribution. In this note we introduce a distribution that generalizes the standard Frechet distribution in the same way the exponentiated exponential distribution generalizes the standard exponential distribution. We refer to this new distribution as the exponentiated Frechet distribution. The aim of this note is to provide a comprehensive treatment of the mathematical properties of this new distribution. We derive the analytical shapes of the corresponding probability density function and the hazard rate function and provide graphical illustrations. We calculate expressions for the $n$th moment and the asymptotic distribution of the extreme order statistics. We investigate the variation of the skewness and kurtosis measures. We also discuss estimation by the method of maximum likelihood.

Authors:
Saralees Nadarajah, snadaraj@chuma1.cas.usf.edu
Samuel Kotz, kotz@seas.gwu.edu

Editor: Rao Chaganty,rchagant@odu.edu

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