The Poisson-Lindley difference model with application to discrete stock price change

Abstract

This paper is devoted to the properties and applications of a new discrete model on (Formula presented.). This model represents the difference of two independent Poisson-Lindley random variables with the same common parameter. The properties, such as, distribution function, moments, quantile function and order statistics are studied. Among its features, it is revealed to be useful for the analysis of overdispersed data sets and also has a flexible probability mass function which is unimodal in nature. Estimation of its parameter by the method of maximum likelihood is obtained. Efficiency of this model with several pertinent competitive models is proved by applying the proposed model to a data set on the change of the stock price. Thanks to its discrete nature, the changes in stock price represent a set of discrete values which suits the nature of the proposed model.