| // 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 num_traits::Float; |
| use crate::{Distribution, OpenClosed01}; |
| use rand::Rng; |
| use core::fmt; |
| |
| /// 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<F> |
| where F: Float, OpenClosed01: Distribution<F> |
| { |
| scale: F, |
| inv_neg_shape: F, |
| } |
| |
| /// 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 fmt::Display for Error { |
| fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { |
| f.write_str(match self { |
| Error::ScaleTooSmall => "scale is not positive in Pareto distribution", |
| Error::ShapeTooSmall => "shape is not positive in Pareto distribution", |
| }) |
| } |
| } |
| |
| #[cfg(feature = "std")] |
| impl std::error::Error for Error {} |
| |
| impl<F> Pareto<F> |
| where F: Float, OpenClosed01: Distribution<F> |
| { |
| /// 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: F, shape: F) -> Result<Pareto<F>, Error> { |
| let zero = F::zero(); |
| |
| if !(scale > zero) { |
| return Err(Error::ScaleTooSmall); |
| } |
| if !(shape > zero) { |
| return Err(Error::ShapeTooSmall); |
| } |
| Ok(Pareto { |
| scale, |
| inv_neg_shape: F::from(-1.0).unwrap() / shape, |
| }) |
| } |
| } |
| |
| impl<F> Distribution<F> for Pareto<F> |
| where F: Float, OpenClosed01: Distribution<F> |
| { |
| fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F { |
| let u: F = OpenClosed01.sample(rng); |
| self.scale * u.powf(self.inv_neg_shape) |
| } |
| } |
| |
| #[cfg(test)] |
| mod tests { |
| use super::*; |
| |
| #[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); |
| } |
| } |
| |
| #[test] |
| fn value_stability() { |
| fn test_samples<F: Float + core::fmt::Debug, D: Distribution<F>>( |
| distr: D, zero: F, expected: &[F], |
| ) { |
| let mut rng = crate::test::rng(213); |
| let mut buf = [zero; 4]; |
| for x in &mut buf { |
| *x = rng.sample(&distr); |
| } |
| assert_eq!(buf, expected); |
| } |
| |
| test_samples(Pareto::new(1.0, 1.0).unwrap(), 0f32, &[ |
| 1.0423688, 2.1235929, 4.132709, 1.4679428, |
| ]); |
| test_samples(Pareto::new(2.0, 0.5).unwrap(), 0f64, &[ |
| 9.019295276219136, |
| 4.3097126018270595, |
| 6.837815045397157, |
| 105.8826669383772, |
| ]); |
| } |
| } |