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Statistics[Distributions][Cauchy] - Cauchy distribution
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Calling Sequence
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Cauchy(a, b)
CauchyDistribution(a, b)
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Parameters
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a
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location parameter
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b
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scale parameter
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Description
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The Cauchy distribution is a continuous probability distribution with probability density function given by:
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subject to the following conditions:
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The Cauchy distribution does not have any defined moments or cumulants.
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The Cauchy variate Cauchy(a,b) is related to the standardized variate Cauchy(0,1) by Cauchy(a,b) ~ a + b * Cauchy(0,1).
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The ratio of two independent unit Normal variates  and  is distributed according to the standard Cauchy variate: Cauchy(0,1) ~ N / M
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The standard Cauchy variate Cauchy(0,1) is a special case of the StudentT variate with one degree of freedom: Cauchy(0,1) ~ StudentT(1).
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Note that the Cauchy command is inert and should be used in combination with the RandomVariable command.
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Examples
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References
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Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
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Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
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Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics.6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
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