Jones, M. C.
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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|
|Keywords:||Cauchy distribution; double-angle for- mulas; functions of normal random variables; spherical symmetry.|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics|
|Depositing User:||Sarah Frain|
|Date Deposited:||26 Apr 2011 11:02|
|Last Modified:||26 Apr 2011 11:02|
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