THE RELATIONSHIP AMONG THE THREE DISTRIBUTIONS: BINOMIAL, POISSON AND NORMAL DISTRIBUTION - Gerald, Banda (American Journal of Statistics and Actuarial Sciences, 2019)
The relationship among the three distributions: Binomial, Poisson and Normal Distribution are of significant interest in many application contexts. Most of the papers in the literature have focused on the relationship among the three distributions based on the definition. In contrast, this paper proposes a simpler approach on how to show the relationship between the Normal distribution and Poisson distribution based on the moment generating function. The study has also proposed the method on how to show that the moment generating function for Poisson distribution can be driven from the moment generating function for Normal distribution when , and the moment generating function for Normal distribution is the same as the Probability Mass Function (PMF) for Poisson distribution. The study has proposed on how to show that the moment generating function for Poisson distribution can be driven from the moment generating function for Binomial distribution.