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.
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Article provided by Elsevier in its journal Statistics & Probability Letters
Volume (Year): 83 (2013)Handle:
Issue (Month): 1 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Related researchKeywords: Self-inverse random variables
; Exchangeable random variables
; Representation of a self-inverse random variable as a ratio
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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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