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.
Volume (Year): 83 (2013)
Issue (Month): 1 ()
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- Jones, M.C., 2008. "The distribution of the ratio X/Y for all centred elliptically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 572-573, March.
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