The asymptotic central-raw ratios for binomial, Poisson and normal distributions

Abstract

The n-th central-raw ratios of random variable with non-zero expectation are considered in this article. Hayman’s method for expansion of the entire function is used to derive the asymptotic formulas of the n-th raw and central moments for binomial and Poisson distributions. Laplace’s expansion of integral is used to obtain the asymptotic formula of the n-th raw moment for normal distribution. Consequently, the n-th central-raw ratios are shown to be infinitesimal with different patterns for binomial Poisson and normal distributions, respectively.