Weighted geometric distribution with new characterizations of geometric distribution

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 derive some distributional properties like moments, generating functions, hazard function and infinite divisibility followed by three methods of estimation of the parameters. A new characterisation of Geometric distribution have also been presented using the proposed distribution. Finally, we examine the model with real data sets.

An Extension of the Geometric Distribution with Properties and Applications

“…The weighted geometric distribution discussed in Bhati and Savitri (2018) having the following mass function.…”

Insights on the trend of the Novel Coronavirus 2019 series in some Small Island Developing States: A Thinning-based Modelling Approach

“…The WCG stems from the family of discrete models that uses a weighted function of a standard discrete-valued probability model [9] , [8] , [10] , [7] , [13] , [34] , [35] , [36] and is expressed as: provided that exists. Here, is the Geometric probability function, that is, , where and .…”

The Cos-Poisson model with a novel count regression analysis

“…These techniques aim to create flexible distributions by the use of a tuning weight function and a well-established (simple) baseline distribution. For further details, we may refer the reader to Patil and Rao [13,14] for the general formalism with discussions, Castillo and Casany [6] for the Poisson distribution as a baseline, Bhati and Joshi [4] for the geometric distribution as a baseline and Bakouch [3] for the negative binomial Lindley distribution as a baseline, and the references therein. The mathematical backgrounds of the discrete weighted distributions can be formulated as follows.…”

“…The most used kind of weight function is the polynomial one, i.e., w(x) = x, w(x) = w(x; r) = x r or w(x) = w(x; a, r) = (x + a) r , with success in count data modeling. On this topic, we again refer to Castillo and Casany [6] for the Poisson distribution and Bhati and Joshi [4] for the geometric distribution.…”