Introducing a New Lifetime Distribution of Power Series Distribution of the Family Gampertz

In this Paper, We propose a new three-parameter lifetime of Power Series distributions of the Family Gampertz with decreasing, increasing, increasing-decreasing and unimodal Shape failure rate. The distribution is a Compound version of of the Gampertz and Zero-truncated Possion distributions, called the Gampertz-Possion distribution (GPD). The density function, the hazard rate function, a general expansion for moments, the density of the order statistic, and the maen and median deviations of the GPD are derived and studied in detail. The maximum likelihood estimation procedure is discussed and an algorithm EM is provided for estimating the parameters. The asymptotic confidence Intervals for the parameters are also obtained based on asymptotic variance covariance matrix.