Analysis of Count Data by Transmuted Geometric Distribution

Abstract

Transmuted geometric distribution (TGD) was recently introduced and investigated by Chakraborty and Bhati [Stat. Oper. Res. Trans. 40 (2016), 153–176]. This is a flexible extension of geometric distribution having an additional parameter that determines its zero inflation as well as the tail length. In the present article we further study this distribution for some of its reliability, stochastic ordering and parameter estimation properties. In parameter estimation among others we discuss an EM algorithm and the performance of estimators is evaluated through extensive simulation. For assessing the statistical significance of additional parameter α, Likelihood ratio test, the Rao's score tests and the Wald's test are developed and its empirical power via simulation are compared. We have demonstrate two applications of (TGD) in modeling real life count data.

Keywords

• Transmuted geometric distribution
• EM algorithm
• Likelihood Ratio test
• Rao score's test
• Wald's test