Independent variables with independent sum and difference: S1-case

Y. Baryshnikov, B. Eisenberg, W. Stadje

Research output: Contribution to journalArticlepeer-review


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 2π 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.

Original languageEnglish (US)
Pages (from-to)161-170
Number of pages10
JournalJournal of Multivariate Analysis
Issue number2
StatePublished - May 1993
Externally publishedYes


  • Characteristic sequences
  • Independent sum and difference
  • Probability measures on groups
  • Wrapped normal distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Independent variables with independent sum and difference: S1-case'. Together they form a unique fingerprint.

Cite this