# On Zero-Inflated Alternative Hyper-Poisson Distribution

## DOI:

https://doi.org/10.6092/issn.1973-2201/9338## Keywords:

Confluent hypergeometric function, Count data models, Generalized likelihood ratio test, Horn-Appel function, Maximum likelihood estimation, Model selection, Simulation## Abstract

Here we develop a zero-inflated version of the alternative hyper-Poisson distribution and discuss its important statistical properties such as probability generating function, expressions for mean, variance, factorial moments, skewness, kurtosis, recursion formula for probabilities, raw moments and factorial moments. Then the maximum likelihood estimation of the parameters of the zero-inflated alternative hyper-Poisson distribution is discussed and certain test procedures are constructed for testing the significance of the inflation parameter. All the procedures are illustrated with the help of certain real life data sets. Moreover, a brief simulation study is carried out for assessing the performances

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*Statistica*,

*81*(4), 423–446. https://doi.org/10.6092/issn.1973-2201/9338

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