Reflected Generalized Beta Inverse Weibull Distribution: definition and properties

Abstract

In this paper we study a broad class of distribution functions which is defined by means of reflected generalized beta distribution. This class includes that of Beta-generated distribution as a special case. In particular, we use this class to extend the Inverse Weibull distribution in order to obtain the Reflected Generalized Beta Inverse Weibull Distribution.For this new distribution, moments, entropy, order statistics and a reliability measure are derived. The link between the Inverse Weibull and the Dagum distribution is generalized. Then the maximum likelihood estimators of the parameters are examined and the observed Fisher information matrix provided. Finally, the usefulness of the model is illustrated by means of an application to real data.