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Self-inverse and exchangeable random variables

Author

Listed:
  • Cacoullos, Theophilos
  • Papadatos, Nickos

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.

Suggested Citation

  • Cacoullos, Theophilos & Papadatos, Nickos, 2013. "Self-inverse and exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 9-12.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:9-12
    DOI: 10.1016/j.spl.2012.06.032
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    References listed on IDEAS

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    1. 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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