### 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 language | English |
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Pages (from-to) | 161-170 |

Number of pages | 10 |

Journal | Journal of Multivariate Analysis |

Volume | 45 |

Issue number | 2 |

DOIs | |

Publication status | Published - May 1993 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty

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## Cite this

Baryshnikov, Y., Eisenberg, B., & Stadje, W. (1993). Independent variables with independent sum and difference: S

^{1}-case.*Journal of Multivariate Analysis*,*45*(2), 161-170. https://doi.org/10.1006/jmva.1993.1031