Jones, M. C.
(1999).
*The American Statistician*, 53(2) pp. 99–102.

URL: | http://www.jstor.org/stable/2685725 |
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Google Scholar: | Look up in Google Scholar |

## Abstract

The polar representation of a pair (X, Y) of spherically symmetrically distributed random variables provides an attractive route to the known fact that their ratio has a Cauchy distribution. In this note, a variety of other distributional relationships involving X and Y is observed to arise very straightforwardly from the simplest of trigonometric formulas, namely multiple-of-angle formulas and sum-of-angles formulas. Cos and sin formulas yield functions of X and Y-which may be independent standard normals-that have the same distribution as X, and tan formulas yield functions of Cauchy variables that remain Cauchy distributed.

Item Type: | Journal Item |
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Copyright Holders: | 1999 American Statistical Association |

ISSN: | 0003-1305 |

Keywords: | Cauchy distribution; double-angle for- mulas; functions of normal random variables; spherical symmetry. |

Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 23926 |

Depositing User: | Sarah Frain |

Date Deposited: | 26 Apr 2011 11:02 |

Last Modified: | 01 May 2019 13:16 |

URI: | http://oro.open.ac.uk/id/eprint/23926 |

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