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use crate::distribution::{Continuous, Gamma, Univariate}; use rand::distributions::Distribution; use rand::Rng; use crate::statistics::*; use crate::Result; /// Implements the [Erlang](https://en.wikipedia.org/wiki/Erlang_distribution) /// distribution /// which is a special case of the /// [Gamma](https://en.wikipedia.org/wiki/Gamma_distribution) /// distribution /// /// # Examples /// /// ``` /// use statrs::distribution::{Erlang, Continuous}; /// use statrs::statistics::Mean; /// use statrs::prec; /// /// let n = Erlang::new(3, 1.0).unwrap(); /// assert_eq!(n.mean(), 3.0); /// assert!(prec::almost_eq(n.pdf(2.0), 0.270670566473225383788, 1e-15)); /// ``` #[derive(Debug, Copy, Clone, PartialEq)] pub struct Erlang { g: Gamma, } impl Erlang { /// Constructs a new erlang distribution with a shape (k) /// of `shape` and a rate (λ) of `rate` /// /// # Errors /// /// Returns an error if `shape` or `rate` are `NaN`. /// Also returns an error if `shape == 0` or `rate <= 0.0` /// /// # Examples /// /// ``` /// use statrs::distribution::Erlang; /// /// let mut result = Erlang::new(3, 1.0); /// assert!(result.is_ok()); /// /// result = Erlang::new(0, 0.0); /// assert!(result.is_err()); /// ``` pub fn new(shape: u64, rate: f64) -> Result<Erlang> { Gamma::new(shape as f64, rate).map(|g| Erlang { g: g }) } /// Returns the shape (k) of the erlang distribution /// /// # Examples /// /// ``` /// use statrs::distribution::Erlang; /// /// let n = Erlang::new(3, 1.0).unwrap(); /// assert_eq!(n.shape(), 3); /// ``` pub fn shape(&self) -> u64 { self.g.shape() as u64 } /// Returns the rate (λ) of the erlang distribution /// /// # Examples /// /// ``` /// use statrs::distribution::Erlang; /// /// let n = Erlang::new(3, 1.0).unwrap(); /// assert_eq!(n.rate(), 1.0); /// ``` pub fn rate(&self) -> f64 { self.g.rate() } } impl Distribution<f64> for Erlang { fn sample<R: Rng + ?Sized>(&self, r: &mut R) -> f64 { Distribution::sample(&self.g, r) } } impl Univariate<f64, f64> for Erlang { /// Calculates the cumulative distribution function for the erlang /// distribution /// at `x` /// /// # Formula /// /// ```ignore /// γ(k, λx) (k - 1)! /// ``` /// /// where `k` is the shape, `λ` is the rate, and `γ` is the lower /// incomplete gamma function fn cdf(&self, x: f64) -> f64 { self.g.cdf(x) } } impl Min<f64> for Erlang { /// Returns the minimum value in the domain of the /// erlang distribution representable by a double precision /// float /// /// # Formula /// /// ```ignore /// 0 /// ``` fn min(&self) -> f64 { self.g.min() } } impl Max<f64> for Erlang { /// Returns the maximum value in the domain of the /// erlang distribution representable by a double precision /// float /// /// # Formula /// /// ```ignore /// INF /// ``` fn max(&self) -> f64 { self.g.max() } } impl Mean<f64> for Erlang { /// Returns the mean of the erlang distribution /// /// # Remarks /// /// Returns `shape` if `rate == f64::INFINITY`. This behavior /// is borrowed from the Math.NET implementation /// /// # Formula /// /// ```ignore /// k / λ /// ``` /// /// where `k` is the shape and `λ` is the rate fn mean(&self) -> f64 { self.g.mean() } } impl Variance<f64> for Erlang { /// Returns the variance of the erlang distribution /// /// # Formula /// /// ```ignore /// k / λ^2 /// ``` /// /// where `α` is the shape and `λ` is the rate fn variance(&self) -> f64 { self.g.variance() } /// Returns the standard deviation of the erlang distribution /// /// # Formula /// /// ```ignore /// sqrt(k) / λ /// ``` /// /// where `k` is the shape and `λ` is the rate fn std_dev(&self) -> f64 { self.g.std_dev() } } impl Entropy<f64> for Erlang { /// Returns the entropy of the erlang distribution /// /// # Formula /// /// ```ignore /// k - ln(λ) + ln(Γ(k)) + (1 - k) * ψ(k) /// ``` /// /// where `k` is the shape, `λ` is the rate, `Γ` is the gamma function, /// and `ψ` is the digamma function fn entropy(&self) -> f64 { self.g.entropy() } } impl Skewness<f64> for Erlang { /// Returns the skewness of the erlang distribution /// /// # Formula /// /// ```ignore /// 2 / sqrt(k) /// ``` /// /// where `k` is the shape fn skewness(&self) -> f64 { self.g.skewness() } } impl Mode<f64> for Erlang { /// Returns the mode for the erlang distribution /// /// # Remarks /// /// Returns `shape` if `rate ==f64::INFINITY`. This behavior /// is borrowed from the Math.NET implementation /// /// # Formula /// /// ```ignore /// (k - 1) / λ /// ``` /// /// where `k` is the shape and `λ` is the rate fn mode(&self) -> f64 { self.g.mode() } } impl Continuous<f64, f64> for Erlang { /// Calculates the probability density function for the erlang distribution /// at `x` /// /// # Remarks /// /// Returns `NAN` if any of `shape` or `rate` are `INF` /// or if `x` is `INF` /// /// # Formula /// /// ```ignore /// (λ^k / Γ(k)) * x^(k - 1) * e^(-λ * x) /// ``` /// /// where `k` is the shape, `λ` is the rate, and `Γ` is the gamma function fn pdf(&self, x: f64) -> f64 { self.g.pdf(x) } /// Calculates the log probability density function for the erlang /// distribution /// at `x` /// /// # Remarks /// /// Returns `NAN` if any of `shape` or `rate` are `INF` /// or if `x` is `INF` /// /// # Formula /// /// ```ignore /// ln((λ^k / Γ(k)) * x^(k - 1) * e ^(-λ * x)) /// ``` /// /// where `k` is the shape, `λ` is the rate, and `Γ` is the gamma function fn ln_pdf(&self, x: f64) -> f64 { self.g.ln_pdf(x) } } #[cfg_attr(rustfmt, rustfmt_skip)] #[cfg(test)] mod test { use std::f64; use crate::distribution::Erlang; use crate::distribution::internal::*; fn try_create(shape: u64, rate: f64) -> Erlang { let n = Erlang::new(shape, rate); assert!(n.is_ok()); n.unwrap() } fn create_case(shape: u64, rate: f64) { let n = try_create(shape, rate); assert_eq!(shape, n.shape()); assert_eq!(rate, n.rate()); } fn bad_create_case(shape: u64, rate: f64) { let n = Erlang::new(shape, rate); assert!(n.is_err()); } #[test] fn test_create() { create_case(1, 0.1); create_case(1, 1.0); create_case(10, 10.0); create_case(10, 1.0); create_case(10, f64::INFINITY); } #[test] fn test_bad_create() { bad_create_case(0, 1.0); bad_create_case(1, 0.0); bad_create_case(1, f64::NAN); bad_create_case(1, -1.0); } #[test] fn test_continuous() { test::check_continuous_distribution(&try_create(1, 2.5), 0.0, 20.0); test::check_continuous_distribution(&try_create(2, 1.5), 0.0, 20.0); test::check_continuous_distribution(&try_create(3, 0.5), 0.0, 20.0); } }