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

Abstract

Poisson-G family is extended to propose beta Poisson-G family of distribution. Useful expansions of the probability density function and the cumulative distribution function of the proposed family are derived as infinite mixtures of the Poisson-G distribution. Moment generating function, power moments, entropy, quantile function, skewness and kurtosis are investigated. Illustrative numerical computation of moments, skewness, kurtosis and entropy are tabulated for select parameter values. Estimation of model parameters by methods of maximum likelihood is discussed. A simulation experiment is carried out under varying sample size to assess the performance of estimation. Finally, suitability check of the proposed model in comparison to a few recently introduced ones is carried out by considering two life time data sets modeling.