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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);
+ }
+ }
+}