A Zero-Truncated Poisson-Aradhana Distribution with Applications

Abstract

In this paper, a zero-truncation of Poisson-Aradhana distribution proposed by Shanker (2017) named ‘zero-truncated Poisson-Aradhana distribution' has been introduced and investigated. A general expression for the r th factorial moment about origin has been obtained and thus the first four moments about origin and the central moments have been given. Also, the expressions for coefficient of variation, skewness, kurtosis, and the index of dispersion of the distribution have been presented and their natures have been discussed graphically. The method of moments and the method of maximum likelihood estimation have also been discussed for estimating its parameter. Two examples of observed real datasets have been given to test the goodness of fit of of the proposed distribution over zero-truncated Poisson-Sujatha distribution, zero-truncated Poisson-Lindley distribution and zero-truncated Poisson distribution.

Keywords and phrases. Zero-truncated distribution, Poisson-Aradhana distribution, Moments, Mathematical and statistical properties, Estimation of parameter, Goodness of fit.

2010 Mathematics Subject Classification. 62E05, 62E99