On Some Properties and Applications of Rayleigh hyper-Poisson Distribution

The Rayleigh distribution is one of the most popular models suitable for analyzing skewed data. In this article, we consider an extended version of the Rayleigh distribution constructed through compounding the Rayleigh distribution with the zero truncated hyper-Poisson distribution. Several properties of the distribution are obtained and discussed the maximum likelihood estimation of the parameters of the distribution, utilizing the method of EM algorithm. The proposed model enjoys both increasing and upside down bathtub failure rate shapes and consequently, it will be suitable for modeling complex data sets. Certain applications of the proposed model are also highlighted with the help of real life data sets. In addition, a simulation study is carried out for assessing the efficiency of the estimators of the parameters.