The family of lifetime and power-series distributions

In this study,we introduce the family of lifetime distributions by compounding any proper continuous lifetime distribution and truncated power-series (PS) distribution, named the family of lifetime-power series distributions (FPS). This new family of distributions contains several lifetime distributions such as generalized exponential (GE), generalized Weibull (GW), generalized Rayleigh (GR), inverse Weibull (IW) and many continuous distributions by compounding of PS distributions. The FPS distributions have decreasing, increasing, decreasing-increasing failure rate. The properties of the proposed family are discussed. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. A formal equation for Fisher information matrix is derived in order to obtaining the asymptotic covariance matrix. The experimental results are illustrated based on real data sets