Some Results for Beta Frechet Distribution

Nadarajah and Gupta (2004) introduced the beta Frechet (BF) distribution, which is a generalization of the exponentiated Frechet (EF) and Frechet distributions, and obtained the probability density and cumulative distribution functions. However, they did not investigate the moments and the order statistics. In this article, the BF density function and the density function of the order statistics are expressed as linear combinations of Frechet density functions. This is important to obtain some mathematical properties of the BF distribution in terms of the corresponding properties of the Frechet distribution. We derive explicit expansions for the ordinary moments and L-moments and obtain the order statistics and their moments. We also discuss maximum likelihood estimation and calculate the information matrix which was not given in the literature. The information matrix is numerically determined. The usefulness of the BF distribution is illustrated through two applications to real data sets.