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User:BRichtigen/Cauchy distribution (view source)
Revision as of 16:58, December 26, 2008
, 16:58, December 26, 2008Cauchy distribution - a start.
[[Image:Cauchy-experiment.png|750px|thumb|Generating Cauchy distributed random numbers]]
Imagine a two-headed arrow circling in a vertical plane around its center, which is fixed on a pole of length 1m. Almost always, one head will point to a line at the bottom of the pole. Measure the distances in one direction as positive, and in the other as negative. If you stop the arrow, it points to a real number.
Stopping the arrow randomly yields a random number. This random number will follow the standard '''Cauchy distribution'''.
Alternatively: if '''U''' is a uniformly distributed random variable on [0, 2 π], then tan('''U''') is standard Cauchy distributed.
Imagine a two-headed arrow circling in a vertical plane around its center, which is fixed on a pole of length 1m. Almost always, one head will point to a line at the bottom of the pole. Measure the distances in one direction as positive, and in the other as negative. If you stop the arrow, it points to a real number.
Stopping the arrow randomly yields a random number. This random number will follow the standard '''Cauchy distribution'''.
Alternatively: if '''U''' is a uniformly distributed random variable on [0, 2 π], then tan('''U''') is standard Cauchy distributed.