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| 1 | +// Copyright 2016-2017 The Rust Project Developers. See the COPYRIGHT |
| 2 | +// file at the top-level directory of this distribution and at |
| 3 | +// https://rust-lang.org/COPYRIGHT. |
| 4 | +// |
| 5 | +// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or |
| 6 | +// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license |
| 7 | +// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your |
| 8 | +// option. This file may not be copied, modified, or distributed |
| 9 | +// except according to those terms. |
| 10 | + |
| 11 | +//! The binomial distribution. |
| 12 | +
|
| 13 | +use Rng; |
| 14 | +use distributions::Distribution; |
| 15 | +use distributions::log_gamma::log_gamma; |
| 16 | +use std::f64::consts::PI; |
| 17 | + |
| 18 | +/// The binomial distribution `Binomial(n, p)`. |
| 19 | +/// |
| 20 | +/// This distribution has density function: `f(k) = n!/(k! (n-k)!) p^k (1-p)^(n-k)` for `k >= 0`. |
| 21 | +/// |
| 22 | +/// # Example |
| 23 | +/// |
| 24 | +/// ```rust |
| 25 | +/// use rand::distributions::{Binomial, Distribution}; |
| 26 | +/// |
| 27 | +/// let bin = Binomial::new(20, 0.3); |
| 28 | +/// let v = bin.sample(&mut rand::thread_rng()); |
| 29 | +/// println!("{} is from a binomial distribution", v); |
| 30 | +/// ``` |
| 31 | +#[derive(Clone, Copy, Debug)] |
| 32 | +pub struct Binomial { |
| 33 | + n: u64, // number of trials |
| 34 | + p: f64, // probability of success |
| 35 | +} |
| 36 | + |
| 37 | +impl Binomial { |
| 38 | + /// Construct a new `Binomial` with the given shape parameters |
| 39 | + /// `n`, `p`. Panics if `p <= 0` or `p >= 1`. |
| 40 | + pub fn new(n: u64, p: f64) -> Binomial { |
| 41 | + assert!(p > 0.0, "Binomial::new called with `p` <= 0"); |
| 42 | + assert!(p < 1.0, "Binomial::new called with `p` >= 1"); |
| 43 | + Binomial { n: n, p: p } |
| 44 | + } |
| 45 | +} |
| 46 | + |
| 47 | +impl Distribution<u64> for Binomial { |
| 48 | + fn sample<R: Rng>(&self, rng: &mut R) -> u64 { |
| 49 | + // binomial distribution is symmetrical with respect to p -> 1-p, k -> n-k |
| 50 | + // switch p so that it is less than 0.5 - this allows for lower expected values |
| 51 | + // we will just invert the result at the end |
| 52 | + let p = if self.p <= 0.5 { |
| 53 | + self.p |
| 54 | + } else { |
| 55 | + 1.0 - self.p |
| 56 | + }; |
| 57 | + |
| 58 | + // expected value of the sample |
| 59 | + let expected = self.n as f64 * p; |
| 60 | + |
| 61 | + let result = |
| 62 | + // for low expected values we just simulate n drawings |
| 63 | + if expected < 25.0 { |
| 64 | + let mut lresult = 0.0; |
| 65 | + for _ in 0 .. self.n { |
| 66 | + if rng.gen::<f64>() < p { |
| 67 | + lresult += 1.0; |
| 68 | + } |
| 69 | + } |
| 70 | + lresult |
| 71 | + } |
| 72 | + // high expected value - do the rejection method |
| 73 | + else { |
| 74 | + // prepare some cached values |
| 75 | + let float_n = self.n as f64; |
| 76 | + let ln_fact_n = log_gamma(float_n + 1.0); |
| 77 | + let pc = 1.0 - p; |
| 78 | + let log_p = p.ln(); |
| 79 | + let log_pc = pc.ln(); |
| 80 | + let sq = (expected * (2.0 * pc)).sqrt(); |
| 81 | + |
| 82 | + let mut lresult; |
| 83 | + |
| 84 | + loop { |
| 85 | + let mut comp_dev: f64; |
| 86 | + // we use the lorentzian distribution as the comparison distribution |
| 87 | + // f(x) ~ 1/(1+x/^2) |
| 88 | + loop { |
| 89 | + // draw from the lorentzian distribution |
| 90 | + comp_dev = (PI*rng.gen::<f64>()).tan(); |
| 91 | + // shift the peak of the comparison ditribution |
| 92 | + lresult = expected + sq * comp_dev; |
| 93 | + // repeat the drawing until we are in the range of possible values |
| 94 | + if lresult >= 0.0 && lresult < float_n + 1.0 { |
| 95 | + break; |
| 96 | + } |
| 97 | + } |
| 98 | + |
| 99 | + // the result should be discrete |
| 100 | + lresult = lresult.floor(); |
| 101 | + |
| 102 | + let log_binomial_dist = ln_fact_n - log_gamma(lresult+1.0) - |
| 103 | + log_gamma(float_n - lresult + 1.0) + lresult*log_p + (float_n - lresult)*log_pc; |
| 104 | + // this is the binomial probability divided by the comparison probability |
| 105 | + // we will generate a uniform random value and if it is larger than this, |
| 106 | + // we interpret it as a value falling out of the distribution and repeat |
| 107 | + let comparison_coeff = (log_binomial_dist.exp() * sq) * (1.2 * (1.0 + comp_dev*comp_dev)); |
| 108 | + |
| 109 | + if comparison_coeff >= rng.gen() { |
| 110 | + break; |
| 111 | + } |
| 112 | + } |
| 113 | + |
| 114 | + lresult |
| 115 | + }; |
| 116 | + |
| 117 | + // invert the result for p < 0.5 |
| 118 | + if p != self.p { |
| 119 | + self.n - result as u64 |
| 120 | + } else { |
| 121 | + result as u64 |
| 122 | + } |
| 123 | + } |
| 124 | +} |
| 125 | + |
| 126 | +#[cfg(test)] |
| 127 | +mod test { |
| 128 | + use distributions::Distribution; |
| 129 | + use super::Binomial; |
| 130 | + |
| 131 | + #[test] |
| 132 | + fn test_binomial() { |
| 133 | + let binomial = Binomial::new(150, 0.1); |
| 134 | + let mut rng = ::test::rng(123); |
| 135 | + let mut sum = 0; |
| 136 | + for _ in 0..1000 { |
| 137 | + sum += binomial.sample(&mut rng); |
| 138 | + } |
| 139 | + let avg = (sum as f64) / 1000.0; |
| 140 | + println!("Binomial average: {}", avg); |
| 141 | + assert!((avg - 15.0).abs() < 0.5); // not 100% certain, but probable enough |
| 142 | + } |
| 143 | + |
| 144 | + #[test] |
| 145 | + #[should_panic] |
| 146 | + #[cfg_attr(target_env = "msvc", ignore)] |
| 147 | + fn test_binomial_invalid_lambda_zero() { |
| 148 | + Binomial::new(20, 0.0); |
| 149 | + } |
| 150 | + #[test] |
| 151 | + #[should_panic] |
| 152 | + #[cfg_attr(target_env = "msvc", ignore)] |
| 153 | + fn test_binomial_invalid_lambda_neg() { |
| 154 | + Binomial::new(20, -10.0); |
| 155 | + } |
| 156 | +} |
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