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

/*!
The t-distribution arises in statistics. If Y_1 has a normal distribution and Y_2 has a chi-squared distribution with \nu degrees of freedom then the ratio,

X = { Y_1 \over \sqrt{Y_2 / \nu} }

has a t-distribution t(x;\nu) with \nu degrees of freedom.
!*/

/// This function computes the probability density p(x) at x for a t-distribution with nu degrees of freedom, using the formula given above.
#[doc(alias = "gsl_ran_tdist_pdf")]
pub fn tdist_pdf(x: f64, nu: f64) -> f64 {
    unsafe { sys::gsl_ran_tdist_pdf(x, nu) }
}

/// This function computes the cumulative distribution functions P(x), Q(x) and their inverses for the t-distribution with nu degrees of freedom.
#[doc(alias = "gsl_cdf_tdist_P")]
pub fn tdist_P(x: f64, nu: f64) -> f64 {
    unsafe { sys::gsl_cdf_tdist_P(x, nu) }
}

/// This function computes the cumulative distribution functions P(x), Q(x) and their inverses for the t-distribution with nu degrees of freedom.
#[doc(alias = "gsl_cdf_tdist_Q")]
pub fn tdist_Q(x: f64, nu: f64) -> f64 {
    unsafe { sys::gsl_cdf_tdist_Q(x, nu) }
}

/// This function computes the cumulative distribution functions P(x), Q(x) and their inverses for the t-distribution with nu degrees of freedom.
#[doc(alias = "gsl_cdf_tdist_Pinv")]
pub fn tdist_Pinv(P: f64, nu: f64) -> f64 {
    unsafe { sys::gsl_cdf_tdist_Pinv(P, nu) }
}

/// This function computes the cumulative distribution functions P(x), Q(x) and their inverses for the t-distribution with nu degrees of freedom.
#[doc(alias = "gsl_cdf_tdist_Qinv")]
pub fn tdist_Qinv(Q: f64, nu: f64) -> f64 {
    unsafe { sys::gsl_cdf_tdist_Qinv(Q, nu) }
}