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20.18 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).

— Function: 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.
— Function: double gsl_cdf_fdist_P (double x, double nu1, double nu2)
— Function: double gsl_cdf_fdist_Q (double x, double nu1, double nu2)
— Function: double gsl_cdf_fdist_Pinv (double P, double nu1, double nu2)
— Function: double gsl_cdf_fdist_Qinv (double Q, double nu1, double nu2)

These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the F-distribution with nu1 and nu2 degrees of freedom.