Struct statrs::distribution::Erlang

pub struct Erlang { /* fields omitted */ }

Implements the Erlang distribution which is a special case of the Gamma distribution

Examples

use statrs::distribution::{Erlang, Continuous};
use statrs::statistics::Distribution;
use statrs::prec;

let n = Erlang::new(3, 1.0).unwrap();
assert_eq!(n.mean().unwrap(), 3.0);
assert!(prec::almost_eq(n.pdf(2.0), 0.270670566473225383788, 1e-15));

Implementations

impl Erlang

pub fn new(shape: u64, rate: f64) -> Result<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 shape(&self) -> u64

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 rate(&self) -> f64

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);

Trait Implementations

impl Clone for Erlang

fn clone(&self) -> Erlang

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Continuous<f64, f64> for Erlang

fn pdf(&self, x: f64) -> f64

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

(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

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

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

impl ContinuousCDF<f64, f64> for Erlang

fn cdf(&self, x: f64) -> f64

Calculates the cumulative distribution function for the erlang distribution at x

Formula

γ(k, λx)  (k - 1)!

where k is the shape, λ is the rate, and γ is the lower incomplete gamma function

fn inverse_cdf(&self, p: T) -> K

Due to issues with rounding and floating-point accuracy the default implementation may be ill-behaved. Specialized inverse cdfs should be used whenever possible. Performs a binary search on the domain of cdf to obtain an approximation of F^-1(p) := inf { x | F(x) >= p }. Needless to say, performance may may be lacking.

impl Debug for Erlang

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Distribution<f64> for Erlang

fn mean(&self) -> Option<f64>

Returns the mean of the erlang distribution

Remarks

Returns shape if rate == f64::INFINITY. This behavior is borrowed from the Math.NET implementation

Formula

k / λ

where k is the shape and λ is the rate

fn variance(&self) -> Option<f64>

Returns the variance of the erlang distribution

Formula

k / λ^2

where α is the shape and λ is the rate

fn entropy(&self) -> Option<f64>

Returns the entropy of the erlang distribution

Formula

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 skewness(&self) -> Option<f64>

Returns the skewness of the erlang distribution

Formula

2 / sqrt(k)

where k is the shape

fn std_dev(&self) -> Option<T>

Returns the standard deviation, if it exists.

impl Distribution<f64> for Erlang

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.

impl Max<f64> for Erlang

fn max(&self) -> f64

Returns the maximum value in the domain of the erlang distribution representable by a double precision float

Formula

INF

impl Min<f64> for Erlang

fn min(&self) -> f64

Returns the minimum value in the domain of the erlang distribution representable by a double precision float

Formula

0

impl Mode<Option<f64>> for Erlang

fn mode(&self) -> Option<f64>

Returns the mode for the erlang distribution

Remarks

Returns shape if rate ==f64::INFINITY. This behavior is borrowed from the Math.NET implementation

Formula

(k - 1) / λ

where k is the shape and λ is the rate

impl PartialEq<Erlang> for Erlang

fn eq(&self, other: &Erlang) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Erlang) -> bool

This method tests for !=.

impl Copy for Erlang

impl StructuralPartialEq for Erlang