Volume 33 • Number 1 • 2010   • On The Poisson Difference Distribution Inference and Applications Abdulhamid A. Alzaid and Maha A. Omair Abstract. The distribution of the difference between two independent Poisson random variables involves the modified Bessel function of the first kind. Using properties of this function, maximum likelihood estimates of the parameters of the Poisson difference 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 testing using likelihood ratio tests was considered. Some new formulas concerning the modified Bessel function of the first kind were provided. Alternative formulas for the probability mass function of the Poisson difference (PD) distribution are introduced. Finally, two new applications for the PD distribution are presented. The first is from the Saudi stock exchange (TASI) and the second is from Dallah hospital. 2000 Mathematics Subject Classification: Primary 60E05; Secondary 62F86, 46N30. Full text: PDF