Self-inverse and exchangeable random variables

A random variable Z will be called self-inverse if it has the same distribution as its reciprocal Z−1. It is shown that if Z is defined as a ratio, X/Y, of two rv’s X and Y (with P[X=0]=P[Y=0]=0), then Z is self-inverse if and only if X and Y are (or can be chosen to be) exchangeable. In general, however, there may not exist iid X and Y in the ratio representation of Z.

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Year of publication:	2013
Authors:	Cacoullos, Theophilos ; Papadatos, Nickos
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 83.2013, 1, p. 9-12
Publisher:	Elsevier
Subject:	Self-inverse random variables \| Exchangeable random variables \| Representation of a self-inverse random variable as a ratio

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

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