Self-Inverse and Exchangeable Random Variables
Methodology
2016-11-18 v2
Abstract
A random variable Z will be called self-inverse if it has the same distribution as its reciprocal 1/Z. 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 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.
Cite
@article{arxiv.1204.1633,
title = {Self-Inverse and Exchangeable Random Variables},
author = {Theophilos Cacoullos and Nickos Papadatos},
journal= {arXiv preprint arXiv:1204.1633},
year = {2016}
}
Comments
Statistics and Probability Letters (to appear, 6 pages)