Analysis of Count Data by Transmuted Geometric Distribution

TL;DR

This paper explores the properties, estimation methods, and applications of the transmuted geometric distribution, a flexible model for count data with zero inflation and tail variation, including simulation studies and real data examples.

Contribution

It provides a comprehensive analysis of TGD's reliability, stochastic ordering, parameter estimation, and significance testing, extending prior work with new methods and applications.

Findings

EM algorithm for parameter estimation developed

Likelihood ratio, Rao's score, and Wald tests evaluated via simulation

Demonstrated applications in real-life count data modeling

Abstract

Transmuted geometric distribution (TGD) was recently introduced and investigated by Chakraborty and Bhati (2016). 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, Likelihood ratio test, the Rao's score tests and the Wald's test are developed and its empirical power via simulation were compared. We have demonstrate two applications of (TGD) in modeling real life count data.