A New Generalization of Weighted Geometric Distribution and its Properties

Abstract

Discrete distributions are widely used to model lifetime for count data. In this paper we introduce a new generalization of weighted geometric (GWG) distribution with the weight function w(x) = (1−p^{αx})^β whose special case proposes a discrete generalized weighted exponential distribution. Further, it is observed that GWG distribution can be produced through a selection model. GWG distribution can be viewed as the generalization of a weighted geometric distribution, the discrete generalized exponential distribution and the classic geometric distribution. We shall study several distributional and structural properties of our distribution such as its shape properties, unimodality, infinite divisibility, moments probability weighted moments, stochastic orderings, order statistics, entropies and stress-strength reliability function. We shall also present some related novel characterizations. Finally, estimation of the parameters are investigated and applicability of the model is examined using a real data set.

Keywords

• Entropy
• Moment
• Moment generating function
• Stress-strength reliability function
• Stochastic orders
• Order statistics