// 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 PERT distribution.
use num_traits::Float;
use crate::{Beta, Distribution, Exp1, Open01, StandardNormal};
use rand::Rng;
use core::fmt;
/// The PERT distribution.
///
/// Similar to the [`Triangular`] distribution, the PERT distribution is
/// parameterised by a range and a mode within that range. Unlike the
/// [`Triangular`] distribution, the probability density function of the PERT
/// distribution is smooth, with a configurable weighting around the mode.
///
/// # Example
///
/// ```rust
/// use rand_distr::{Pert, Distribution};
///
/// let d = Pert::new(0., 5., 2.5).unwrap();
/// let v = d.sample(&mut rand::thread_rng());
/// println!("{} is from a PERT distribution", v);
/// ```
///
/// [`Triangular`]: crate::Triangular
#[derive(Clone, Copy, Debug)]
#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
pub struct Pert<F>
where
F: Float,
StandardNormal: Distribution<F>,
Exp1: Distribution<F>,
Open01: Distribution<F>,
{
min: F,
range: F,
beta: Beta<F>,
}
/// Error type returned from [`Pert`] constructors.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum PertError {
/// `max < min` or `min` or `max` is NaN.
RangeTooSmall,
/// `mode < min` or `mode > max` or `mode` is NaN.
ModeRange,
/// `shape < 0` or `shape` is NaN
ShapeTooSmall,
}
impl fmt::Display for PertError {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
f.write_str(match self {
PertError::RangeTooSmall => "requirement min < max is not met in PERT distribution",
PertError::ModeRange => "mode is outside [min, max] in PERT distribution",
PertError::ShapeTooSmall => "shape < 0 or is NaN in PERT distribution",
})
}
}
#[cfg(feature = "std")]
#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
impl std::error::Error for PertError {}
impl<F> Pert<F>
where
F: Float,
StandardNormal: Distribution<F>,
Exp1: Distribution<F>,
Open01: Distribution<F>,
{
/// Set up the PERT distribution with defined `min`, `max` and `mode`.
///
/// This is equivalent to calling `Pert::new_shape` with `shape == 4.0`.
#[inline]
pub fn new(min: F, max: F, mode: F) -> Result<Pert<F>, PertError> {
Pert::new_with_shape(min, max, mode, F::from(4.).unwrap())
}
/// Set up the PERT distribution with defined `min`, `max`, `mode` and
/// `shape`.
pub fn new_with_shape(min: F, max: F, mode: F, shape: F) -> Result<Pert<F>, PertError> {
if !(max > min) {
return Err(PertError::RangeTooSmall);
}
if !(mode >= min && max >= mode) {
return Err(PertError::ModeRange);
}
if !(shape >= F::from(0.).unwrap()) {
return Err(PertError::ShapeTooSmall);
}
let range = max - min;
let mu = (min + max + shape * mode) / (shape + F::from(2.).unwrap());
let v = if mu == mode {
shape * F::from(0.5).unwrap() + F::from(1.).unwrap()
} else {
(mu - min) * (F::from(2.).unwrap() * mode - min - max) / ((mode - mu) * (max - min))
};
let w = v * (max - mu) / (mu - min);
let beta = Beta::new(v, w).map_err(|_| PertError::RangeTooSmall)?;
Ok(Pert { min, range, beta })
}
}
impl<F> Distribution<F> for Pert<F>
where
F: Float,
StandardNormal: Distribution<F>,
Exp1: Distribution<F>,
Open01: Distribution<F>,
{
#[inline]
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
self.beta.sample(rng) * self.range + self.min
}
}
#[cfg(test)]
mod test {
use super::*;
#[test]
fn test_pert() {
for &(min, max, mode) in &[
(-1., 1., 0.),
(1., 2., 1.),
(5., 25., 25.),
] {
let _distr = Pert::new(min, max, mode).unwrap();
// TODO: test correctness
}
for &(min, max, mode) in &[
(-1., 1., 2.),
(-1., 1., -2.),
(2., 1., 1.),
] {
assert!(Pert::new(min, max, mode).is_err());
}
}
}
