Asymptotic expansions in the approximation by the Poisson law
The objective of this paper is to obtain asymptotic expansions for the distribution \(F_{nk_n} (x)\) of sums of series of mutually independent in each series random variables, converging to the Poisson law. The authors do not assume the integrability of the random variables and construct asymptotic expansions for the distributions of sums of such variables. In doing so, they impose conditions on the growth of finite order factorial moments of random variables. In the proof they use the method of characteristic functions. In addition, they consider the case where the random variables are integral and nonnegative.
scientific article; zbMATH DE number 939536