The Cauchy Distribution¶
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gsl_ran_cauchy(a)¶
This function returns a random variate from the Cauchy distribution with scale parameter
a. The probability distribution for Cauchy random variates is,\[p(x) dx = {1 \over a\pi (1 + (x/a)^2) } dx\]for \(x\) in the range \(-\infty\) to \(+\infty\). The Cauchy distribution is also known as the Lorentz distribution.
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gsl_ran_cauchy_pdf(x, a)¶
This function computes the probability density \(p(x)\) at \(x\) for a Cauchy distribution with scale parameter
a, using the formula given above.
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gsl_ran_cauchy_P(x, a)¶
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gsl_ran_cauchy_Q(x, a)¶
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gsl_ran_cauchy_Pinv(P, a)¶
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gsl_ran_cauchy_Qinv(Q, a)¶
These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the Cauchy distribution with scale parameter
a.