The F-distribution
The F-distribution arises in statistics. If Y_1 and Y_2
are chi-squared deviates with \nu_1 and \nu_2 degrees of
freedom then the ratio,
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.