## File: The-Cauchy-Distribution.html

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 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111  GNU Scientific Library – Reference Manual: The Cauchy Distribution

20.9 The Cauchy Distribution

Function: double gsl_ran_cauchy (const gsl_rng * r, double 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.

Function: double gsl_ran_cauchy_pdf (double x, double a)

This function computes the probability density p(x) at x for a Cauchy distribution with scale parameter a, using the formula given above.

Function: double gsl_cdf_cauchy_P (double x, double a)
Function: double gsl_cdf_cauchy_Q (double x, double a)
Function: double gsl_cdf_cauchy_Pinv (double P, double a)
Function: double gsl_cdf_cauchy_Qinv (double Q, double a)

These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Cauchy distribution with scale parameter a.