LIMIT THEOREMS FOR POWER-SERIES DISTRIBUTIONS WITH FINITE RADIUS OF CONVERGENCE

作     者：Timashev, A. N. 

作者机构：Inst Cryptog Telecommun & Comp Sci Moscow Russia 

出 版 物：《THEORY OF PROBABILITY AND ITS APPLICATIONS》 (概率论及其应用)

年 卷 期：2018年第63卷第1期

页      面：45-56页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：power-series distributions radius of convergence triangular arrays gamma-distribution weak convergence 

摘      要：Sufficient conditions for the weak convergence of the distributions of the random variables (1 - x)xi(x) as x - 1- to the limiting gamma-distribution are put forward. The random variable e x has power-series distribution with radius of convergence 1 and parameter x is an element of (0, 1). Limit theorems for the probabilities P{xi(x )= k} are proposed. Asymptotic expansions of local probabilities are derived for sums of independent identically distributed variables with the same distribution as xi(x) in a triangular array with x - 1-. For the corresponding general allocation scheme, local limit theorems for the joint distributions of the occupancies of the cells are obtained.