The Exponentiated Hypoexponential Disribution

TL;DR

This paper introduces the Exponentiated Hypoexponential Distribution, deriving its key functions, discussing parameter estimation, and demonstrating its effectiveness through real data fitting.

Contribution

It extends the hypoexponential distribution by adding a parameter, providing explicit formulas, and applying it to real data for the first time.

Findings

Derived closed-form expressions for distribution functions.

Developed maximum likelihood estimators for parameters.

Successfully fitted the distribution to real data, outperforming competitors.

Abstract

In this paper we study the Exponentiated Hypoexponential Distribution with different parameters. The distribution added a parameter to the n parameters of the Hypoexponenial distribution. We first derive a closed expression of the probability density function and the cumulative distribution function of Maximum Exponentiated Exponential distribution. These functions are used to determine an exact expression of the probability density function, the cumulative function, reliability function, and hazard function of our Exponentiated Hypoexponential Distribution. We discuss estimation of the parameters by maximum likelihood estimators. The distribution has been fitted to a real life data set and the fit has been found to be a serious competitor to the others.