A connection between self-normalized products and stable laws

Let X1,...,Xn constitute a random sample from a population with underpinning cumulative distribution function F(x). For any value 0<[alpha]<1, we prove that under a condition of stable laws, the self-normalized product follows the same distribution as X1, where [summation operator]* denotes the sum of over all permissible sequences of integers 1[less-than-or-equals, slant]i1<i2<...<in-1[less-than-or-equals, slant]n.

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Year of publication:	2007
Authors:	Melnykov, Igor ; Chen, John T.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 77.2007, 17, p. 1662-1665
Publisher:	Elsevier
Keywords:	Self-normalized product Stable law Symmetric distribution Rayleigh model Random walk Data transformation

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://ebvufind01.dmz1.zbw.eu/10005137833