18.17 The F-distribution

X = { (Y_1 / \nu_1) \over (Y_2 / \nu_2) }

has an F-distribution F(x;\nu_1,\nu_2).

Random: double gsl_ran_fdist (const gsl_rng * r, double nu1, double nu2)

This function returns a random variate from the F-distribution with degrees of freedom nu1 and nu2. The distribution function is,

p(x) dx = { \Gamma((\nu_1 + \nu_2)/2) \over \Gamma(\nu_1/2) \Gamma(\nu_2/2) } \nu_1^{\nu_1/2} \nu_2^{\nu_2/2} x^{\nu_1/2 - 1} (\nu_2 + \nu_1 x)^{-\nu_1/2 -\nu_2/2}

for x >= 0.

Function: double gsl_ran_fdist_pdf (double x, double nu1, double nu2)

This function computes the probability density p(x) at x for an F-distribution with nu1 and nu2 degrees of freedom, using the formula given above.