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8.4.14 The Cauchy distribution

The probability density function for the Cauchy distribution: cauchy cauchyd

The cauchy (or cauchyd) command computes the probability density function for the Cauchy distribution (sometimes called the Lorentz distribution).

Examples

The cumulative distribution function for the Cauchy distribution: cauchy_cdf cauchyd_cdf

The cauchy_cdf (or cauchyd_cdf) command computes the cumulative distribution function for the Cauchy distribution.

It turns out that cauchy_cdf(a,b,x) = 1/2 + arctan((xa)/b)/π.

Examples

The inverse distribution function for the Cauchy distribution: cauchy_icdf cauchyd_icdf

The cauchy_icdf (or cauchyd_icdf) command computes the inverse distribution for the Cauchy distribution.

Example

cauchy_icdf(2,3,0.23)

Output:

−1.40283204777

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