Self-inverse and exchangeable random variables

Theophilos Cacoullos and Nickos Papadatos

Statistics & Probability Letters, 2013, vol. 83, issue 1, 9-12

Abstract: 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.

Keywords: Self-inverse random variables; Exchangeable random variables; Representation of a self-inverse random variable as a ratio (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spl.2012.06.032

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