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// Copyright 2022 The Ferric AI Project Developers
use rand::Rng;
use rand_distr::Distribution as Distribution2;
use rand_distr::Gumbel as Gumbel2;
use crate::distributions::Distribution;
/// Gumbel (type-I extreme value) distribution over the reals.
///
/// The PDF is
///
/// $$p(x \mid \mu, \beta) =
/// \frac{1}{\beta}\exp\!\left(-\frac{x-\mu}{\beta}
/// - e^{-(x-\mu)/\beta}\right)$$
///
/// where $\mu \in \mathbb{R}$ is the location parameter and $\beta > 0$ is
/// the scale parameter.
///
/// See [Gumbel distribution](https://en.wikipedia.org/wiki/Gumbel_distribution)
/// on Wikipedia for further details.
///
/// # Examples
///
/// ```
/// use ferric::distributions::{Distribution, Gumbel};
/// use rand::thread_rng;
///
/// let dist = Gumbel::new(0.0, 1.0).unwrap();
/// let x: f64 = dist.sample(&mut thread_rng());
/// println!("sample = {:.4}", x);
/// ```
pub struct Gumbel {
mu: f64,
beta: f64,
}
impl Gumbel {
/// Construct a Gumbel distribution with location `mu` ($\mu$) and
/// scale `beta` ($\beta$).
///
/// # Errors
///
/// Returns `Err` if `beta` is not strictly positive.
pub fn new(mu: f64, beta: f64) -> Result<Gumbel, String> {
if beta <= 0.0 {
Err(format!(
"Gumbel: illegal scale `{}` should be greater than 0",
beta
))
} else {
Ok(Gumbel { mu, beta })
}
}
}
impl<R: Rng + ?Sized> Distribution<R> for Gumbel {
type Domain = f64;
fn sample(&self, rng: &mut R) -> f64 {
Gumbel2::new(self.mu, self.beta).unwrap().sample(rng)
}
/// Returns $-(x-\mu)/\beta - e^{-(x-\mu)/\beta} - \ln\beta$.
fn log_prob(&self, x: &f64) -> f64 {
let z = (x - self.mu) / self.beta;
-z - (-z).exp() - self.beta.ln()
}
fn is_discrete(&self) -> bool {
false
}
}
impl std::fmt::Display for Gumbel {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(f, "Gumbel {{ mu = {}, beta = {} }}", self.mu, self.beta)
}
}
#[cfg(test)]
mod tests {
use super::*;
use rand::rngs::ThreadRng;
use rand::thread_rng;
#[test]
fn gumbel_sample() {
let mut rng = thread_rng();
let mu = 1.0f64;
let beta = 2.0f64;
let dist = Gumbel::new(mu, beta).unwrap();
println!("dist = {}", dist);
let trials = 100_000;
let mut total = 0.0f64;
for _ in 0..trials {
total += dist.sample(&mut rng);
}
let empirical_mean = total / trials as f64;
// Mean = mu + beta * Euler–Mascheroni constant ≈ mu + beta * 0.5772
let expected_mean = mu + beta * 0.577_215_664_9;
// Std = beta * pi / sqrt(6)
let std = beta * std::f64::consts::PI / 6.0f64.sqrt();
let err = 5.0 * std / (trials as f64).sqrt();
assert!((empirical_mean - expected_mean).abs() < err);
}
#[test]
fn gumbel_log_prob() {
// Gumbel(0, 1) at x=0: z=0, log_prob = 0 - 1 - 0 = -1
let dist = Gumbel::new(0.0, 1.0).unwrap();
let lp = <Gumbel as Distribution<ThreadRng>>::log_prob(&dist, &0.0);
assert!((lp - (-1.0f64)).abs() < 1e-10);
assert!(!<Gumbel as Distribution<ThreadRng>>::is_discrete(&dist));
}
#[test]
fn gumbel_display() {
let dist = Gumbel::new(1.0, 2.0).unwrap();
let s = format!("{}", dist);
assert!(s.contains("Gumbel"), "missing type name: {}", s);
}
#[test]
#[should_panic]
fn gumbel_zero_scale() {
Gumbel::new(0.0, 0.0).unwrap();
}
#[test]
#[should_panic]
fn gumbel_negative_scale() {
Gumbel::new(0.0, -1.0).unwrap();
}
}