On Some Properties of Beta-Generated Distributions

Abstract

This note is concerned with a broad family of univariate distributions, namely the class of the beta-generated distributions which is created on the basis of the beta distribution by incorporating on this classic model a parent distribution function F with respective density f. The class of beta-generated distributions have received a great attention in the recent literature on distribution theory. The aim of this note is to provide with some properties and characterizations of the beta-generated distributions which are already known from the theory of order statistics.