Self-Inverse and Exchangeable Random Variables

Details Self-Inverse and Exchangeable Random Variables Self-Inverse and Exchangeable Random Variables

2012-04-07

arxiv.org/abs/1204.1633v1

Statistics

Methodology

5 pages

Scientific paper

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 Pr[X=0]=Pr[Y=0]=0), then Z is self-inverse iff X and Y are (or can be chosen to be) exchangeable. That is, Z is self-inverse iff there exist exchangeable random variables X and Y so that Z=X/Y. In general it may not be possible for the rv's X and Y, in the ratio representation of Z, to be chosen iid.

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