The Rayleigh Distribution

gsl_ran_rayleigh(sigma)

This function returns a random variate from the Rayleigh distribution with scale parameter sigma. The distribution is,

\[p(x) dx = {x \over \sigma^2} \exp(- x^2/(2 \sigma^2)) dx\]

for \(x > 0\).

gsl_ran_rayleigh_pdf(x, sigma)

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

gsl_ran_rayleigh_P(x, sigma)

gsl_ran_rayleigh_Q(x, sigma)

gsl_ran_rayleigh_Pinv(P, sigma)

gsl_ran_rayleigh_Qinv(Q, sigma)

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

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The Cauchy Distribution

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The Rayleigh Tail Distribution