Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

HOME ALL ARTICLES View

Commun. Korean Math. Soc. 2018; 33(2): 605-618

Online first article April 6, 2018      Printed April 30, 2018

https://doi.org/10.4134/CKMS.c170110

Copyright © The Korean Mathematical Society.

An extension of random summations of independent and identically distributed random variables

Le Truong Giang, Tran Loc Hung

2/4 Tran Xuan Soan Street, 2/4 Tran Xuan Soan Street

Abstract

The main goal of this paper is to study an extension of random summations of independent and identically distributed random variables when the number of summands in random summation is a partial sum of n independent, identically distributed, non-negative integer-valued random variables. Some characterizations of random summations are considered. The central limit theorems and weak law of large numbers for extended random summations are established. Some weak limit theorems related to geometric random sums, binomial random sums and negative-binomial random sums are also investigated as asymptotic behaviors of extended random summations.

Keywords: random summation, central limit theorem, weak law of large numbers, gamma distribution, Laplace distribution

MSC numbers: Primary 60E10; Secondary 60F05