Independent variables with independent sum and difference: S1-case

Y. Baryshnikov, B. Eisenberg, W. Stadje

Research output: Contribution to journalArticle

11 Citations (Scopus)

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 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
Pages (from-to)161-170
Number of pages10
JournalJournal of Multivariate Analysis
Volume45
Issue number2
DOIs
Publication statusPublished - May 1993
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

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