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// Copyright 2018 Developers of the Rand project.
//
// 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 Pareto distribution.
use rand::Rng;
use crate::{Distribution, OpenClosed01};
use crate::utils::Float;
/// Samples floating-point numbers according to the Pareto distribution
///
/// # Example
/// ```
/// use rand::prelude::*;
/// use rand_distr::Pareto;
///
/// let val: f64 = thread_rng().sample(Pareto::new(1., 2.).unwrap());
/// println!("{}", val);
/// ```
#[derive(Clone, Copy, Debug)]
pub struct Pareto<N> {
scale: N,
inv_neg_shape: N,
}
/// Error type returned from `Pareto::new`.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum Error {
/// `scale <= 0` or `nan`.
ScaleTooSmall,
/// `shape <= 0` or `nan`.
ShapeTooSmall,
}
impl<N: Float> Pareto<N>
where OpenClosed01: Distribution<N>
{
/// Construct a new Pareto distribution with given `scale` and `shape`.
///
/// In the literature, `scale` is commonly written as x<sub>m</sub> or k and
/// `shape` is often written as α.
pub fn new(scale: N, shape: N) -> Result<Pareto<N>, Error> {
if !(scale > N::from(0.0)) {
return Err(Error::ScaleTooSmall);
}
if !(shape > N::from(0.0)) {
return Err(Error::ShapeTooSmall);
}
Ok(Pareto { scale, inv_neg_shape: N::from(-1.0) / shape })
}
}
impl<N: Float> Distribution<N> for Pareto<N>
where OpenClosed01: Distribution<N>
{
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
let u: N = OpenClosed01.sample(rng);
self.scale * u.powf(self.inv_neg_shape)
}
}
#[cfg(test)]
mod tests {
use crate::Distribution;
use super::Pareto;
#[test]
#[should_panic]
fn invalid() {
Pareto::new(0., 0.).unwrap();
}
#[test]
fn sample() {
let scale = 1.0;
let shape = 2.0;
let d = Pareto::new(scale, shape).unwrap();
let mut rng = crate::test::rng(1);
for _ in 0..1000 {
let r = d.sample(&mut rng);
assert!(r >= scale);
}
}
}
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