## 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 (US) |
---|---|

Pages (from-to) | 161-170 |

Number of pages | 10 |

Journal | Journal of Multivariate Analysis |

Volume | 45 |

Issue number | 2 |

DOIs | |

State | Published - May 1993 |

Externally published | Yes |

## Keywords

- 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

## Fingerprint

Dive into the research topics of 'Independent variables with independent sum and difference: S^{1}-case'. Together they form a unique fingerprint.