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Independent Variables with Independent Sum and Difference: S1-Case

Author

Listed:
  • Baryshnikov, Y.
  • Eisenberg, B.
  • Stadje, W.

Abstract

A classic result in probability theory states that two independent real-valued random variables having independent sum and difference are either constant or normally distributed with the same variance. In this article conditions are round on independent random variables X and Y taking values in the group of real numbers modulo 2[pi] so that X +Y and X - Y are independent. When X and Y are identically distributed, the small number of possible distributions for which X and Y have the desired property is known. In the general case there is a richer family of possible distributions for X and Y.

Suggested Citation

  • Baryshnikov, Y. & Eisenberg, B. & Stadje, W., 1993. "Independent Variables with Independent Sum and Difference: S1-Case," Journal of Multivariate Analysis, Elsevier, vol. 45(2), pages 161-170, May.
    • Handle: RePEc:eee:jmvana:v:45:y:1993:i:2:p:161-170
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