1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117

use crate::core::*;
use rand::Rng;
use spaces::continuous::PositiveReals;
use std::fmt;

#[derive(Debug, Clone, Copy)]
pub struct InvGamma {
    pub alpha: f64,
    pub beta: f64,
}

impl InvGamma {
    pub fn new(alpha: f64, beta: f64) -> InvGamma {
        assert_positive_real!(alpha);
        assert_positive_real!(beta);

        InvGamma { alpha, beta }
    }

    pub fn with_scale(k: f64, theta: f64) -> InvGamma {
        InvGamma::new(k, 1.0 / theta)
    }
}

impl Default for InvGamma {
    fn default() -> InvGamma {
        InvGamma {
            alpha: 1.0,
            beta: 1.0,
        }
    }
}

impl Distribution for InvGamma {
    type Support = PositiveReals;

    fn support(&self) -> PositiveReals {
        PositiveReals
    }

    fn cdf(&self, x: f64) -> Probability {
        use special_fun::FloatSpecial;

        (self.alpha.gammainc(self.beta / x) / self.alpha.gamma()).into()
    }

    fn sample<R: Rng + ?Sized>(&self, _: &mut R) -> f64 {
        unimplemented!()
    }
}

impl ContinuousDistribution for InvGamma {
    fn pdf(&self, x: f64) -> Probability {
        use special_fun::FloatSpecial;

        (self.beta.powf(self.alpha) * x.powf(-self.alpha - 1.0) * (-self.beta / x).exp()
            / self.alpha.gamma())
        .into()
    }
}

impl UnivariateMoments for InvGamma {
    fn mean(&self) -> f64 {
        if self.alpha <= 1.0 {
            unimplemented!("Mean is undefined for alpha <= 1.")
        }

        self.beta / (self.alpha - 1.0)
    }

    fn variance(&self) -> f64 {
        if self.alpha <= 2.0 {
            unimplemented!("Variance is undefined for alpha <= 2.")
        }

        let am1 = self.alpha - 1.0;

        self.beta * self.beta / am1 / am1 / (self.alpha - 2.0)
    }

    fn skewness(&self) -> f64 {
        if self.alpha <= 3.0 {
            unimplemented!("Skewness is undefined for alpha <= 3.")
        }

        4.0 * (self.alpha - 2.0).sqrt() / (self.alpha - 3.0)
    }

    fn excess_kurtosis(&self) -> f64 {
        if self.alpha <= 4.0 {
            unimplemented!("Kurtosis is undefined for alpha <= 4.")
        }

        (30.0 * self.alpha - 66.0) / (self.alpha - 3.0) / (self.alpha - 4.0)
    }
}

impl Modes for InvGamma {
    fn modes(&self) -> Vec<f64> {
        vec![self.beta / (self.alpha + 1.0)]
    }
}

impl Entropy for InvGamma {
    fn entropy(&self) -> f64 {
        use special_fun::FloatSpecial;

        self.alpha + (self.beta * self.alpha.gamma()).ln()
            - (1.0 + self.alpha) * self.alpha.digamma()
    }
}

impl fmt::Display for InvGamma {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(f, "Inv-Gamma({}, {})", self.alpha, self.beta)
    }
}