## File: The-F_002ddistribution.html

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 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121  GNU Scientific Library – Reference Manual: The F-distribution

20.19 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.