probability 0.16.0

use distribution;
use source::Source;

/// An exponential distribution.
#[derive(Clone, Copy, Debug)]
pub struct Exponential {
    lambda: f64,
}

impl Exponential {
    /// Create an exponential distribution with rate `lambda`.
    ///
    /// It should hold that `lambda > 0`.
    #[inline]
    pub fn new(lambda: f64) -> Self {
        should!(lambda > 0.0);
        Exponential { lambda: lambda }
    }

    /// Return the rate parameter.
    #[inline(always)]
    pub fn lambda(&self) -> f64 {
        self.lambda
    }
}

impl distribution::Continuous for Exponential {
    #[inline]
    fn density(&self, x: f64) -> f64 {
        if x < 0.0 {
            0.0
        } else {
            self.lambda * (-self.lambda * x).exp()
        }
    }
}

impl distribution::Distribution for Exponential {
    type Value = f64;

    #[inline]
    fn distribution(&self, x: f64) -> f64 {
        if x <= 0.0 {
            0.0
        } else {
            -(-self.lambda * x).exp_m1()
        }
    }
}

impl distribution::Entropy for Exponential {
    #[inline]
    fn entropy(&self) -> f64 {
        1.0 - self.lambda.ln()
    }
}

impl distribution::Inverse for Exponential {
    #[inline]
    fn inverse(&self, p: f64) -> f64 {
        should!(0.0 <= p && p <= 1.0);
        -(-p).ln_1p() / self.lambda
    }
}

impl distribution::Kurtosis for Exponential {
    #[inline]
    fn kurtosis(&self) -> f64 {
        6.0
    }
}

impl distribution::Mean for Exponential {
    #[inline]
    fn mean(&self) -> f64 {
        self.lambda.recip()
    }
}

impl distribution::Median for Exponential {
    #[inline]
    fn median(&self) -> f64 {
        use std::f64::consts::LN_2;
        self.lambda.recip() * LN_2
    }
}

impl distribution::Modes for Exponential {
    #[inline]
    fn modes(&self) -> Vec<f64> {
        vec![0.0]
    }
}

impl distribution::Sample for Exponential {
    #[inline]
    fn sample<S>(&self, source: &mut S) -> f64
    where
        S: Source,
    {
        -source.read::<f64>().ln() / self.lambda
    }
}

impl distribution::Skewness for Exponential {
    #[inline]
    fn skewness(&self) -> f64 {
        2.0
    }
}

impl distribution::Variance for Exponential {
    #[inline]
    fn variance(&self) -> f64 {
        self.lambda.powi(-2)
    }

    #[inline]
    fn deviation(&self) -> f64 {
        self.lambda.recip()
    }
}

#[cfg(test)]
mod tests {
    use assert;
    use prelude::*;

    macro_rules! new(
        ($lambda:expr) => (Exponential::new($lambda));
    );

    #[test]
    fn density() {
        let d = new!(2.0);
        let x = vec![-1.0, 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, 6.0, 12.0];
        let p = vec![
            0.000000000000000e+00,
            2.000000000000000e+00,
            7.357588823428847e-01,
            2.706705664732254e-01,
            9.957413673572789e-02,
            3.663127777746836e-02,
            1.347589399817093e-02,
            4.957504353332717e-03,
            6.709252558050237e-04,
            1.228842470665642e-05,
            7.550269088558195e-11,
        ];

        assert::close(
            &x.iter().map(|&x| d.density(x)).collect::<Vec<_>>(),
            &p,
            1e-15,
        );
    }

    #[test]
    fn distribution() {
        let d = new!(2.0);
        let x = vec![
            -1.0, 0.0, 0.01, 0.05, 0.1, 0.15, 0.25, 0.5, 1.0, 1.5, 2.0, 3.0, 4.0,
        ];
        let p = vec![
            0.000000000000000e+00,
            0.000000000000000e+00,
            1.980132669324470e-02,
            9.516258196404043e-02,
            1.812692469220182e-01,
            2.591817793182821e-01,
            3.934693402873666e-01,
            6.321205588285577e-01,
            8.646647167633873e-01,
            9.502129316321360e-01,
            9.816843611112658e-01,
            9.975212478233336e-01,
            9.996645373720975e-01,
        ];

        assert::close(
            &x.iter().map(|&x| d.distribution(x)).collect::<Vec<_>>(),
            &p,
            1e-15,
        );
    }

    #[test]
    fn entropy() {
        use std::f64::consts::E;
        assert_eq!(new!(E).entropy(), 0.0);
    }

    #[test]
    fn inverse() {
        use std::f64::INFINITY;

        let d = new!(2.0);
        let x = vec![
            0.0, 0.01, 0.05, 0.1, 0.15, 0.25, 0.5, 1.0, 1.5, 2.0, 3.0, 4.0, INFINITY,
        ];
        let p = vec![
            0.000000000000000e+00,
            1.980132669324470e-02,
            9.516258196404043e-02,
            1.812692469220182e-01,
            2.591817793182821e-01,
            3.934693402873666e-01,
            6.321205588285577e-01,
            8.646647167633873e-01,
            9.502129316321360e-01,
            9.816843611112658e-01,
            9.975212478233336e-01,
            9.996645373720975e-01,
            1.000000000000000e-00,
        ];

        assert::close(
            &p.iter().map(|&p| d.inverse(p)).collect::<Vec<_>>(),
            &x,
            1e-14,
        );
    }

    #[test]
    fn kurtosis() {
        assert_eq!(new!(2.0).kurtosis(), 6.0);
    }

    #[test]
    fn mean() {
        assert_eq!(new!(2.0).mean(), 0.5);
    }

    #[test]
    fn median() {
        use std::f64::consts::LN_2;
        assert_eq!(new!(LN_2).median(), 1.0);
    }

    #[test]
    fn modes() {
        assert_eq!(new!(2.0).modes(), vec![0.0]);
    }

    #[test]
    fn skewness() {
        assert_eq!(new!(2.0).skewness(), 2.0);
    }

    #[test]
    fn variance() {
        assert_eq!(new!(2.0).variance(), 0.25);
    }

    #[test]
    fn deviation() {
        assert_eq!(new!(2.0).deviation(), 0.5);
    }
}