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Distributional relationships arising from simple trigonometric formulas

Jones, M. C. (1999). Distributional relationships arising from simple trigonometric formulas. The American Statistician, 53(2) pp. 99–102.

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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 Article
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/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 23926
Depositing User: Sarah Frain
Date Deposited: 26 Apr 2011 11:02
Last Modified: 26 Apr 2011 11:02
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