Abstract
Here we develop an order k version of the hyper-Poisson distribution and study some of its properties by deriving its probability mass function, mean, variance and recursion formulae for probabilities, raw moments and factorial moments. The estimation of the parameters of this class of distributions by the method of mixed moments and method of maximum likelihood is attempted and it is demonstrated with the help of a real data set that this order k version of the hyper-Poisson distribution fits the situations better than the existing model. DOI: http://dx.doi.org/10.4038/sljastats.v14i1.5876
Highlights
Bardwell and Crow (1964) has obtained a two-parameter generalization of the Poisson distribution, namely the hyper-Poisson distribution, which they defined as in the following
All these estimation and testing procedures are illustrated with the help of a real data and presented in respective sections
The results concerning further statistical inference in connection with the SHPD will be published in the sequel
Summary
Bardwell and Crow (1964) has obtained a two-parameter generalization of the Poisson distribution, namely the hyper-Poisson distribution, which they defined as in the following. A non-negative integer valued random variable X is said to follow the hyper-Poisson distribution (HPD) if its probability mass function (p.m.f.) has the following form. Roohi and Ahmad (2003a) attempted estimation of the parameters of the HPD using negative moments. The estimation of the parameters of the SHPD has been discussed in section 4 by the method of mixed moments using first observed frequency and the method of maximum likelihood. All these estimation and testing procedures are illustrated with the help of a real data and presented in respective sections. The results concerning further statistical inference in connection with the SHPD will be published in the sequel
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