Self-inverse and exchangeable random variables
Date
2013Author
Cacoullos, TheophilosPapadatos, Nickos
Source
Statistics and Probability LettersVolume
83Issue
1Pages
9-12Google Scholar check
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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. © 2012.