  Nadarajah and Gupta (2004) introduced the beta Fr\'echet (BF) distribution,
which is a generalization of the exponentiated Fr\'echet (EF) and Fr\'echet
distributions, and obtained the probability density and cumulative distribution
functions. However, they do not investigated its moments and the order
statistics. In this paper the BF density function and the density function of
the order statistics are expressed as linear combinations of Fr\'echet density
functions. This is important to obtain some mathematical properties of the BF
distribution in terms of the corresponding properties of the Fr\'echet
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 known. The information matrix is easily numerically determined. Two
applications to real data sets are given to illustrate the potentiality of this
distribution.
