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 \(F(x;\nu_1,\nu_2)\).
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gsl_ran_fdist(nu1, 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 \(x \geq 0\).
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gsl_ran_fdist_pdf(x, nu1, 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.
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gsl_cdf_fdist_P(x, nu1, nu2)
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gsl_cdf_fdist_Q(x, nu1, nu2)
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gsl_cdf_fdist_Pinv(P, nu1, nu2)
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gsl_cdf_fdist_Qinv(Q, nu1, 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.