Some Properties of the Positive Hyper-Poisson Distribution and its Applications

C. Satheesh Kumar, Emil Ninan Abraham


In this paper we consider a zero-truncated form of the hyper-Poisson distribution and investigate some of its crucial properties through deriving its probability generating function, cumulative distribution function, expressions for factorial moments, mean, variance and recurrence relations for probabilities, raw moments and factorial moments. Further, the estimation of the parameters of the distribution is discussed. The distribution has been fitted to certain real life data sets to test its goodness of fit. The likelihood ratio test procedure is adopted for checking the significance of the parameters and a simulation study is performed for assessing the efficiency of the maximum likelihood estimators.


Confluent hypergeometric function; Mixed moment estimation; Maximum likelihood estimation; Stirling numbers of the second kind; GLRT; Simulation

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DOI: 10.6092/issn.1973-2201/8658