Alpha Power Poisson-G Distribution With an Application to Bur XII Distribution Lifetime Data

We propose a new method of adding two shape parameters to a family of distributions for more flexibility and wider scope of applications called Alpha power Poisson-g distribution. A special case has been considered in details namely; one parameter exponential distribution. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, moment generating function, mean and median deviation, Bonferroni and Lorenz curve, order statistics and expression of the Renyi entropies are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. Further we consider an extension of the two-parameter Bur XII distribution also, mainly for data analysis purposes. Three data sets have been analyzed to show how the proposed models work in practice. We also carried out Monte Carlo simulation to further investigate the properties of the proposed method of estimation.