Weighted geometric distribution with a new characterisation of geometric distribution

TL;DR

This paper introduces a new generalized geometric distribution, explores its properties, estimation methods, and provides a characterization, supported by real data analysis.

Contribution

It presents a novel generalization of the geometric distribution with a new characterization and comprehensive property analysis.

Findings

Distributional properties derived and discussed

Parameter estimation methods developed and compared

Model validated with real data sets

Abstract

In this paper, we introduce a new generalization of geometric distribution which can also viewed as discrete analogue of weighted exponential distribution introduced by Gupta and Kundu(2009). We study some basic distributional properties like moments, generating functions, hazard function followed by different methods of estimation of the parameters. Characterization of Geometric distribution have also been presented. Finally, we examine the model with real data sets.