Limit distributions for products of sums

Yongcheng Qi

doi:10.1016/S0167-7152(02)00438-8

Limit distributions for products of sums

Yongcheng Qi

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

Let {X,X_n, n ≥ 1} be a sequence of independent and identically distributed positive random variables and set S_n = ∑_j=1ⁿ for n ≥ 1. This paper proves that properly normalized products of the partial sums, (∏_j=1ⁿ S_j/n!μⁿ)^μ/An, converges in distribution to some nondegenerate distribution when X is in the domain of attraction of a stable law with index α ∈ (1,2].

Original language	English (US)
Pages (from-to)	93-100
Number of pages	8
Journal	Statistics and Probability Letters
Volume	62
Issue number	1
DOIs	https://doi.org/10.1016/S0167-7152(02)00438-8
State	Published - Mar 15 2003

Keywords

Limit distribution
Product of sums
Stable laws

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abstract = "Let {X,Xn, n ≥ 1} be a sequence of independent and identically distributed positive random variables and set Sn = ∑j=1n for n ≥ 1. This paper proves that properly normalized products of the partial sums, (∏j=1n Sj/n!μn)μ/An, converges in distribution to some nondegenerate distribution when X is in the domain of attraction of a stable law with index α ∈ (1,2].",

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N2 - Let {X,Xn, n ≥ 1} be a sequence of independent and identically distributed positive random variables and set Sn = ∑j=1n for n ≥ 1. This paper proves that properly normalized products of the partial sums, (∏j=1n Sj/n!μn)μ/An, converges in distribution to some nondegenerate distribution when X is in the domain of attraction of a stable law with index α ∈ (1,2].

AB - Let {X,Xn, n ≥ 1} be a sequence of independent and identically distributed positive random variables and set Sn = ∑j=1n for n ≥ 1. This paper proves that properly normalized products of the partial sums, (∏j=1n Sj/n!μn)μ/An, converges in distribution to some nondegenerate distribution when X is in the domain of attraction of a stable law with index α ∈ (1,2].

KW - Limit distribution

KW - Product of sums

KW - Stable laws

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JO - Statistics and Probability Letters

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