Further Statistical Properties of Size-Biased Geometric Distribution

Abstract

In this article, size biased geometric distribution is introduced. Some of its statistical and reliability properties are discussed like probability function, cumulative distribution and reliability function, hazard rate function and moments. The unknown distribution parameter is obtained by the moments and the maximum likelihood method in a closed form. Monte Carlo simulation study is performed in order to investigate the performance of maximum likelihood estimators. Additionally, this distribution is evaluated for the new count regression model. Real life data which comes from the statistical literature are considered for the illustration and the results are compared with Poisson, geometric, discrete Weibull, discrete Gamma and discrete Lindley distributions.