On the Zhang-power series distributions with application to lifetime modeling

Many recent probability distributions are introduced by compounding the well-known continuous distributions  with the power series distribution.   In this paper, we provide a general closed-form expression  for the cumulative distribution function of this class. Then, we introduce  a new four parameter lifetime distribution called  Zhang-power series (ZPS) distribution. This distribution is very useful in the lifetime, reliability and extreme-value data analysis. The distribution properties including survival function, hazard function and limiting behavior of the probability density  and hazard functions are studied. The method of maximum likelihood estimation is used to estimate the model parameters. Applications to real data sets are given to show the flexibility and potentiality of the proposed model.

Keywords:

maximum likelihood estimation , Monte Carlo simulation , Power series distribution , Zhang distribution