On the Poisson difference distribution inference and applications.

The distribution of the dierence between two independent Poisson random variables involves the modied Bessel function of the rst kind. Using properties of this function, maximum likelihood estimates of the parameters of the Poisson dierence were derived. Asymptotic distribution property of the maximum likelihood estimates is discussed. Maximum likelihood estimates were compared with the moment estimates in a Monte Carlo study. Hypothesis test- ing using likelihood ratio tests was considered. Some new formulas concerning the modied Bessel function of the rst kind were provided. Alternative formu- las for the probability mass function of the Poisson dierence (PD) distribution are introduced. Finally, two new applications for the PD distribution are pre- sented. The rst is from the Saudi stock exchange (TASI) and the second is