A new generalization of the geometric distribution using Azzalini's mechanism: properties and application

TL;DR

This paper introduces a novel generalization of the geometric distribution using Azzalini's skewing mechanism, exploring its properties, estimation methods, and demonstrating its effectiveness on real count data.

Contribution

It is the first application of Azzalini's skewing mechanism to the geometric distribution, providing new structural properties and model comparisons.

Findings

The proposed model outperforms existing models in real data fitting.

Maximum likelihood estimation is effectively applied to the new distribution.

Likelihood ratio tests support the inclusion of the skewing parameter.

Abstract

The skewing mechanism of Azzalini for continuous distributions is used for the first time to derive a new generalization of the geometric distribution. Various structural properties of the proposed distribution are investigated. Characterizations, including a new result for the geometric distribution, in terms of the proposed model are established. Extensive simulation experiment is done to evaluate performance of the maximum likelihood estimation method. Likelihood ratio test for the necessity of additional skewing parameter is derived and corresponding simulation based power study is also reported. Two real life count datasets are analyzed with the proposed model and compared with some recently introduced two-parameter count models. The findings clearly indicate the superiority of the proposed model over the existing ones in modelling real life count data.