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
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147

use crate::prelude::*;
use rand::Rng;
use spaces::real::PositiveReals;
use std::fmt;

shape_params! {
    Params<f64> {
        alpha,
        beta
    }
}

new_dist!(BetaPrime<Params>);

macro_rules! get_params {
    ($self:ident) => { ($self.0.alpha.0, $self.0.beta.0) }
}

impl BetaPrime {
    pub fn new(alpha: f64, beta: f64) -> Result<BetaPrime, failure::Error> {
        Params::new(alpha, beta).map(|p| BetaPrime(p))
    }

    pub fn new_unchecked(alpha: f64, beta: f64) -> BetaPrime {
        BetaPrime(Params::new_unchecked(alpha, beta))
    }
}

impl Default for BetaPrime {
    fn default() -> BetaPrime {
        BetaPrime(Params::new_unchecked(1.0, 1.0))
    }
}

impl Distribution for BetaPrime {
    type Support = PositiveReals;
    type Params = Params;

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

    fn params(&self) -> Params { self.0 }

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

        let (alpha, beta) = get_params!(self);

        Probability::new_unchecked((x / (1.0 + x)).betainc(alpha, beta))
    }

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

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

        let (a, b) = get_params!(self);

        let numerator = x.powf(a - 1.0) * (1.0 + x).powf(-a - b);
        let denominator = a.beta(b);

        numerator / denominator
    }
}

impl UnivariateMoments for BetaPrime {
    fn mean(&self) -> f64 {
        let (a, b) = get_params!(self);

        if b <= 1.0 {
            undefined!("mean is undefined for values of beta <= 1.")
        }

        a / (b - 1.0)
    }

    fn variance(&self) -> f64 {
        let (a, b) = get_params!(self);

        if b <= 2.0 {
            undefined!("variance is undefined for values of beta <= 2.")
        }

        let bm1 = b - 1.0;

        a * (a + bm1) / (b - 2.0) / bm1 / bm1
    }

    fn skewness(&self) -> f64 {
        let (a, b) = get_params!(self);

        if b <= 3.0 {
            undefined!("skewness is undefined for values of beta <= 3.")
        }

        let bm1 = b - 1.0;

        2.0 * (2.0 * a + bm1) / (b - 3.0) * ((b - 2.0) / (a * (a + bm1))).sqrt()
    }

    fn excess_kurtosis(&self) -> f64 {
        let (a, b) = get_params!(self);
        let bm1 = b - 1.0;

        let numerator = 6.0 * (a + bm1) * (5.0 * b - 11.0) + bm1 * bm1 * (b - 2.0);
        let denominator = a * (a + bm1) * (b - 3.0) * (b - 4.0);

        numerator / denominator
    }
}

impl Modes for BetaPrime {
    fn modes(&self) -> Vec<f64> {
        let (a, b) = get_params!(self);

        if a >= 1.0 {
            vec![(a - 1.0) / (b + 1.0)]
        } else {
            vec![0.0]
        }
    }
}

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

        let (a, b) = get_params!(self);
        let apb = a + b;

        a.logbeta(b)
            - (a - 1.0) * a.digamma()
            - (b - 1.0) * b.digamma()
            + (apb - 2.0) * apb.digamma()
    }
}

impl fmt::Display for BetaPrime {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        let (alpha, beta) = get_params!(self);

        write!(f, "BetaPrime({}, {})", alpha, beta)
    }
}