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

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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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10.1016/S0167-7152(02)00438-8

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title = "Limit distributions for products of sums",

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].",

keywords = "Limit distribution, Product of sums, Stable laws",

author = "Yongcheng Qi",

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pages = "93--100",

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T1 - Limit distributions for products of sums

AU - Qi, Yongcheng

PY - 2003/3/15

Y1 - 2003/3/15

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

UR - https://www.scopus.com/pages/publications/0037445509

UR - https://www.scopus.com/pages/publications/0037445509#tab=citedBy

U2 - 10.1016/S0167-7152(02)00438-8

DO - 10.1016/S0167-7152(02)00438-8

M3 - Article

AN - SCOPUS:0037445509

SN - 0167-7152

VL - 62

SP - 93

EP - 100

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 1

ER -

Limit distributions for products of sums

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Keywords

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