A count model based on Mittag-Leffler interarrival times

Abstract

In this paper, a new generalized counting process with Mittag-Leffler inter-arrival time distribution is introduced. This new model is a generalization of the Poisson process. The computational intractability is overcome by deriving the Mittag-Leffler count model using polynomial expansion. The hazard function of this new model is a decreasing function of time, so that the distribution displays negative duration dependence. The model is applied to a data on interarrival times of customers in a bank counter. This new count model can be simulated by Markov Chain Monte-Carlo (MCMC) methods, using Metropolis- Hastings algorithm. Our new model has many nice features such as its closed form nature, computational simplicity, ability to nest Poisson, existence of moments and autocorrelation and can be used for both equi-dispersed and over-dispersed data.