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.
Le Truong Giang, Tran Loc Hung
2/4 Tran Xuan Soan Street, 2/4 Tran Xuan Soan Street
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
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