Beta Poisson-G Family of Distributions: Its Properties and Application with Failure Time Data

TL;DR

This paper introduces the beta Poisson-G family of distributions, exploring its properties, estimation methods, and application to failure time data, demonstrating its effectiveness through simulations and real data comparisons.

Contribution

It presents a new generalized distribution family, derives its properties, and evaluates its performance on real failure time data, expanding modeling options.

Findings

Distribution effectively models failure time data

Estimation methods perform well in simulations

Model comparison shows improved fit over existing models

Abstract

A new generalization of the family of Poisson-G is called beta Poisson-G family of distribution. Useful expansions of the probability density function and the cumulative distribution function of the proposed family are derived and seen as infinite mixtures of the Poisson-G distribution. Moment generating function, power moments, entropy, quantile function, skewness and kurtosis are investigated. Numerical computation of moments, skewness, kurtosis and entropy are tabulated for select parameter values. Furthermore, estimation by methods of maximum likelihood is discussed. A simulation study is carried at under varying sample size to assess the performance of this model. Finally suitability check of the proposed model in comparison to its recently introduced models is carried out by considering two real life data sets modeling.