Products of independent, normally attracted random variables (Q1092503)
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scientific article; zbMATH DE number 4020097
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Products of independent, normally attracted random variables |
scientific article; zbMATH DE number 4020097 |
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Products of independent, normally attracted random variables (English)
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1988
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Let \(R_ n\) denote the correlation coefficient of an n-sample of pairs \((X_ i,Y_ i)\), each distributed as (X,Y). Assume X and Y are independent and in the domain of attraction of the normal law. It is shown that this entails XY being in that domain of attraction, and that \(d_ nR_ n\to N(0,1)\) in distribution for constants \(d_ n\) satisfying lim sup(n\({}^{1/2}/d_ n)\leq 1\). Examples illustrate details of these limit theorems.
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products of random variables
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central limit theorem
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domain of attraction
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slowly varying function
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