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//
// A rust binding for the GSL library by Guillaume Gomez (guillaume1.gomez@gmail.com)
//

/*!
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).
!*/

use ffi;
use types::Rng;

/// This function returns a random variate from the F-distribution with degrees of freedom nu1 and nu2. The distribution function is,
///
/// ```latex
/// 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.
pub fn fdist(r: &Rng, nu1: f64, nu2: f64) -> f64 {
    unsafe { ffi::gsl_ran_fdist(ffi::FFI::unwrap(r), nu1, nu2) }
}

/// This function computes the cumulative distribution functions P(x), Q(x) and their inverses for the F-distribution with nu1 and nu2 degrees of freedom.
pub fn fdist_pdf(x: f64, nu1: f64, nu2: f64) -> f64 {
    unsafe { ffi::gsl_ran_fdist_pdf(x, nu1, nu2) }
}

/// This function computes the cumulative distribution functions P(x), Q(x) and their inverses for the F-distribution with nu1 and nu2 degrees of freedom.
pub fn fdist_P(x: f64, nu1: f64, nu2: f64) -> f64 {
    unsafe { ffi::gsl_cdf_fdist_P(x, nu1, nu2) }
}

/// This function computes the cumulative distribution functions P(x), Q(x) and their inverses for the F-distribution with nu1 and nu2 degrees of freedom.
pub fn fdist_Q(x: f64, nu1: f64, nu2: f64) -> f64 {
    unsafe { ffi::gsl_cdf_fdist_Q(x, nu1, nu2) }
}

/// This function computes the cumulative distribution functions P(x), Q(x) and their inverses for the F-distribution with nu1 and nu2 degrees of freedom.
pub fn fdist_Pinv(P: f64, nu1: f64, nu2: f64) -> f64 {
    unsafe { ffi::gsl_cdf_fdist_Pinv(P, nu1, nu2) }
}

/// This function computes the cumulative distribution functions P(x), Q(x) and their inverses for the F-distribution with nu1 and nu2 degrees of freedom.
pub fn fdist_Qinv(Q: f64, nu1: f64, nu2: f64) -> f64 {
    unsafe { ffi::gsl_cdf_fdist_Qinv(Q, nu1, nu2) }
}