The Beta Generalized Exponential Distribution

TL;DR

This paper introduces the beta generalized exponential distribution, a flexible new model that encompasses existing distributions and offers comprehensive mathematical properties and practical parameter estimation methods.

Contribution

It presents the beta generalized exponential distribution, deriving its key properties and demonstrating its effectiveness in modeling positive data.

Findings

The distribution generalizes beta exponential and generalized exponential distributions.

Derived explicit formulas for moments and order statistics.

Application shows the model's flexibility and effectiveness in real data analysis.

Abstract

We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the $r$th moment thus generalizing some results in the literature. Expressions for the density, moment generating function and $r$th moment of the order statistics also are obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix. We observe in one application to real data set that this model is quite flexible and can be used quite effectively in analyzing positive data in place of the beta exponential and generalized exponential distributions.