| // Copyright 2018 Developers of the Rand project. |
| // Copyright 2016-2017 The Rust Project Developers. |
| // |
| // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or |
| // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license |
| // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your |
| // option. This file may not be copied, modified, or distributed |
| // except according to those terms. |
| |
| //! The binomial distribution. |
| |
| use Rng; |
| use distributions::{Distribution, Bernoulli, Cauchy}; |
| use distributions::utils::log_gamma; |
| |
| /// The binomial distribution `Binomial(n, p)`. |
| /// |
| /// This distribution has density function: |
| /// `f(k) = n!/(k! (n-k)!) p^k (1-p)^(n-k)` for `k >= 0`. |
| /// |
| /// # Example |
| /// |
| /// ``` |
| /// use rand::distributions::{Binomial, Distribution}; |
| /// |
| /// let bin = Binomial::new(20, 0.3); |
| /// let v = bin.sample(&mut rand::thread_rng()); |
| /// println!("{} is from a binomial distribution", v); |
| /// ``` |
| #[derive(Clone, Copy, Debug)] |
| pub struct Binomial { |
| /// Number of trials. |
| n: u64, |
| /// Probability of success. |
| p: f64, |
| } |
| |
| impl Binomial { |
| /// Construct a new `Binomial` with the given shape parameters `n` (number |
| /// of trials) and `p` (probability of success). |
| /// |
| /// Panics if `p < 0` or `p > 1`. |
| pub fn new(n: u64, p: f64) -> Binomial { |
| assert!(p >= 0.0, "Binomial::new called with p < 0"); |
| assert!(p <= 1.0, "Binomial::new called with p > 1"); |
| Binomial { n, p } |
| } |
| } |
| |
| impl Distribution<u64> for Binomial { |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 { |
| // Handle these values directly. |
| if self.p == 0.0 { |
| return 0; |
| } else if self.p == 1.0 { |
| return self.n; |
| } |
| |
| // For low n, it is faster to sample directly. For both methods, |
| // performance is independent of p. On Intel Haswell CPU this method |
| // appears to be faster for approx n < 300. |
| if self.n < 300 { |
| let mut result = 0; |
| let d = Bernoulli::new(self.p); |
| for _ in 0 .. self.n { |
| result += rng.sample(d) as u32; |
| } |
| return result as u64; |
| } |
| |
| // binomial distribution is symmetrical with respect to p -> 1-p, k -> n-k |
| // switch p so that it is less than 0.5 - this allows for lower expected values |
| // we will just invert the result at the end |
| let p = if self.p <= 0.5 { |
| self.p |
| } else { |
| 1.0 - self.p |
| }; |
| |
| // prepare some cached values |
| let float_n = self.n as f64; |
| let ln_fact_n = log_gamma(float_n + 1.0); |
| let pc = 1.0 - p; |
| let log_p = p.ln(); |
| let log_pc = pc.ln(); |
| let expected = self.n as f64 * p; |
| let sq = (expected * (2.0 * pc)).sqrt(); |
| |
| let mut lresult; |
| |
| // we use the Cauchy distribution as the comparison distribution |
| // f(x) ~ 1/(1+x^2) |
| let cauchy = Cauchy::new(0.0, 1.0); |
| loop { |
| let mut comp_dev: f64; |
| loop { |
| // draw from the Cauchy distribution |
| comp_dev = rng.sample(cauchy); |
| // shift the peak of the comparison ditribution |
| lresult = expected + sq * comp_dev; |
| // repeat the drawing until we are in the range of possible values |
| if lresult >= 0.0 && lresult < float_n + 1.0 { |
| break; |
| } |
| } |
| |
| // the result should be discrete |
| lresult = lresult.floor(); |
| |
| let log_binomial_dist = ln_fact_n - log_gamma(lresult+1.0) - |
| log_gamma(float_n - lresult + 1.0) + lresult*log_p + (float_n - lresult)*log_pc; |
| // this is the binomial probability divided by the comparison probability |
| // we will generate a uniform random value and if it is larger than this, |
| // we interpret it as a value falling out of the distribution and repeat |
| let comparison_coeff = (log_binomial_dist.exp() * sq) * (1.2 * (1.0 + comp_dev*comp_dev)); |
| |
| if comparison_coeff >= rng.gen() { |
| break; |
| } |
| } |
| |
| // invert the result for p < 0.5 |
| if p != self.p { |
| self.n - lresult as u64 |
| } else { |
| lresult as u64 |
| } |
| } |
| } |
| |
| #[cfg(test)] |
| mod test { |
| use Rng; |
| use distributions::Distribution; |
| use super::Binomial; |
| |
| fn test_binomial_mean_and_variance<R: Rng>(n: u64, p: f64, rng: &mut R) { |
| let binomial = Binomial::new(n, p); |
| |
| let expected_mean = n as f64 * p; |
| let expected_variance = n as f64 * p * (1.0 - p); |
| |
| let mut results = [0.0; 1000]; |
| for i in results.iter_mut() { *i = binomial.sample(rng) as f64; } |
| |
| let mean = results.iter().sum::<f64>() / results.len() as f64; |
| assert!((mean as f64 - expected_mean).abs() < expected_mean / 50.0); |
| |
| let variance = |
| results.iter().map(|x| (x - mean) * (x - mean)).sum::<f64>() |
| / results.len() as f64; |
| assert!((variance - expected_variance).abs() < expected_variance / 10.0); |
| } |
| |
| #[test] |
| fn test_binomial() { |
| let mut rng = ::test::rng(351); |
| test_binomial_mean_and_variance(150, 0.1, &mut rng); |
| test_binomial_mean_and_variance(70, 0.6, &mut rng); |
| test_binomial_mean_and_variance(40, 0.5, &mut rng); |
| test_binomial_mean_and_variance(20, 0.7, &mut rng); |
| test_binomial_mean_and_variance(20, 0.5, &mut rng); |
| } |
| |
| #[test] |
| fn test_binomial_end_points() { |
| let mut rng = ::test::rng(352); |
| assert_eq!(rng.sample(Binomial::new(20, 0.0)), 0); |
| assert_eq!(rng.sample(Binomial::new(20, 1.0)), 20); |
| } |
| |
| #[test] |
| #[should_panic] |
| fn test_binomial_invalid_lambda_neg() { |
| Binomial::new(20, -10.0); |
| } |
| } |