rv 0.15.0-rc.1

use special::Gamma;

/// Χ<sup>2</sup> (Chi-squared) test.
///
/// # Example
///
/// Test whether the observed counts were generated uniformly.
///
/// ```
/// use rv::misc::x2_test;
///
/// // The observed counts/frequencies
/// let f_obs: Vec<u32> = vec![28, 31, 40, 35];
///
/// // The probability with which each entry should occur
/// let ps: Vec<f64> = vec![0.25; 4];
///
/// let (stat, p) = x2_test(&f_obs, &ps);
/// assert!(p > 0.05);
/// ```
pub fn x2_test(f_obs: &[u32], ps: &[f64]) -> (f64, f64) {
    let k = f_obs.len();
    let nf = f64::from(f_obs.iter().sum::<u32>());
    let x2 = nf
        * f_obs.iter().zip(ps.iter()).fold(0.0, |acc, (&o, &p)| {
            let err_term = f64::from(o) / nf - p;
            acc + err_term * err_term / p
        });

    let df = (k - 1) as f64;
    let p = 1.0 - (x2 / 2.0).inc_gamma(df / 2.0);
    (x2, p)
}

#[cfg(test)]
mod tests {
    use super::*;
    const TOL: f64 = 1E-12;

    #[test]
    fn gof() {
        let f_obs: Vec<u32> = vec![28, 31, 40, 35];
        let ps: Vec<f64> = vec![0.25; 4];
        let (x2, p) = x2_test(&f_obs, &ps);

        assert::close(x2, 2.417_910_447_761_194, TOL);
        assert::close(p, 0.490_309_306_965_388_3, TOL);
    }
}