The Weibull–Conway–Maxwell–Poisson distribution to analyze survival data

In this paper, we consider the distribution of life length of a series system with random number of components, say MM. Considering the distribution of MM as COM–Poisson, a Weibull–COM–Poisson distribution (WCOMP) is developed. The COM–Poisson is a generalization of the Poisson distribution having one extra parameter. The structural properties of the resulting distribution are presented and the maximum likelihood estimation of the parameters is investigated. Extensive simulation studies are carried out to study the performance of the estimates. A score test is developed to test the importance of the extra parameter. For illustration, three real data sets are examined and it is shown that the WCOMP model, presented here, fits better than the exponential Poisson and the exponential-COMP distributions.