On Zero-truncated Alternative Hyper-Poisson Distribution and Its Applications

• Published in: Bulletin - Calcutta Statistical Association Vol. 74; no. 1; pp. 7 - 26
• Main Authors: Kumar, C. Satheesh, Abraham, Emil Ninan
• Format: Journal Article
• Language: English
• Published: New Delhi, India SAGE Publications 01.05.2022
• Subjects: Confluent hypergeometric function; maximum likelihood estimation; Stirling numbers of the second kind; GLRT; simulation
• ISSN: 0008-0683; 2456-6462
• DOI: 10.1177/00080683221094170

Here we propose a zero-truncated version of the alternative hyper-Poisson distribution of Kumar and Nair[1] and study some of its statistical properties. We derive some of its essential properties such as mean, variance, probability generating function, cumulative distribution function, hazard function, an expression for its factorial moments, raw moments and recursion formulae for its probabilities, raw moments and factorial moments. The method of moments and method of maximum likelihood estimation have been discussed for estimating the parameters of the proposed distribution. To check the suitability of the proposed model it has been applied to certain real-life data sets and has shown that it provides a good fitting to the data sets under consideration. Method of generalized likelihood ratio test is employed for examining the significance of the parameter and a brief simulation study is carried out for verifying the efficiency of the moment and maximum likelihood estimators of the parameters of the distribution. AMS subject classification: 60E05; 60E10; 33C20