Struct RandGamma 

pub struct RandGamma<F>
where
    F: Float,
    StandardNormal: Distribution<F>,
    Exp1: Distribution<F>,
    Open01: Distribution<F>,
{ /* private fields */ }

The Gamma distribution Gamma(k, θ).

The Gamma distribution is a continuous probability distribution with shape parameter k > 0 (number of events) and scale parameter θ > 0 (mean waiting time between events). It describes the time until k events occur in a Poisson process with rate 1/θ. It is the generalization of the Exponential distribution.

Density function

f(x) = x^(k - 1) * exp(-x / θ) / (Γ(k) * θ^k) for x > 0, where Γ is the gamma function.

Plot

The following plot illustrates the Gamma distribution with various values of k and θ. Curves with θ = 1 are more saturated, while corresponding curves with θ = 2 have a lighter color.

Example

use rand_distr::{Distribution, Gamma};

let gamma = Gamma::new(2.0, 5.0).unwrap();
let v = gamma.sample(&mut rand::rng());
println!("{} is from a Gamma(2, 5) distribution", v);

Notes

The algorithm used is that described by Marsaglia & Tsang 2000¹, falling back to directly sampling from an Exponential for shape == 1, and using the boosting technique described in that paper for shape < 1.

---

1. George Marsaglia and Wai Wan Tsang. 2000. “A Simple Method for Generating Gamma Variables” ACM Trans. Math. Softw. 26, 3 (September 2000), 363-372. DOI:10.1145/358407.358414 ↩

Implementations

impl<F> Gamma<F>

where F: Float, StandardNormal: Distribution<F>, Exp1: Distribution<F>, Open01: Distribution<F>,

pub fn new(shape: F, scale: F) -> Result<Gamma<F>, Error>

Construct an object representing the Gamma(shape, scale) distribution.

Trait Implementations

impl<F> Clone for Gamma<F>

where F: Clone + Float, StandardNormal: Distribution<F>, Exp1: Distribution<F>, Open01: Distribution<F>,

fn clone(&self) -> Gamma<F>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F> Debug for Gamma<F>

where F: Debug + Float, StandardNormal: Distribution<F>, Exp1: Distribution<F>, Open01: Distribution<F>,

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

Formats the value using the given formatter.

impl<F> Distribution<F> for Gamma<F>

where F: Float, StandardNormal: Distribution<F>, Exp1: Distribution<F>, Open01: Distribution<F>,

fn sample<R>(&self, rng: &mut R) -> F

where R: Rng + ?Sized,

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

fn sample_iter<R>(self, rng: R) -> Iter<Self, R, T>

where R: Rng, Self: Sized,

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

fn map<F, S>(self, func: F) -> Map<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Map sampled values to type S

impl<F> PartialEq for Gamma<F>

where F: PartialEq + Float, StandardNormal: Distribution<F>, Exp1: Distribution<F>, Open01: Distribution<F>,

fn eq(&self, other: &Gamma<F>) -> bool

Tests for self and other values to be equal, and is used by ==.

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

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<F> Copy for Gamma<F>

where F: Copy + Float, StandardNormal: Distribution<F>, Exp1: Distribution<F>, Open01: Distribution<F>,

impl<F> StructuralPartialEq for Gamma<F>

where F: Float, StandardNormal: Distribution<F>, Exp1: Distribution<F>, Open01: Distribution<F>,