In this paper a new compounding distribution with increasing, decreasing, bathtub shaped and unimodal-bathtub shaped hazard rate function. The new three-parameters distribution as a generalization of the exponential power distribution is proposed. Maximum likelihood estimation of the parameters, raw-moments, density function of the order statistics, survival function, hazard rate function, mean residual lifetime, reliability function and median are presented. Then the properties of this distribution are illustrated based on a real data set.

In this paper a new compounding distribution with increasing, decreasing, bathtub shaped and unimodal hazard rate function is proposed. The new four-parameters distribution is a generalization of the complementary exponential power distribution. The raw-moments, density function of the order statistics, survival function, hazard rate function, quantiles, mean residual lifetime and reliability function are presented. The estimation of the new distribution in a special case Poisson complementary exponential power distribution is studied by the method of maximum likelihood and EM algorithm. Expression for asymptotic distribution for the maximum likelihood estimation of the parameters of the PCEP distribution are obtained and for determining the precision of the variance and covariance of the estimations, a simulation is used, Then experimental results are illustrated based on the real data set.