Struct Gamma 

pub struct Gamma<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

When the shape (k) or scale (θ) parameters are close to the upper limits of the floating point type F, the implementation may overflow and produce inf. On the other hand, when k is relatively close to zero (like 0.005) and θ is huge (like 1e200), the implementation is likely be affected by underflow and may fail to produce tiny floating point values (like 1e-200), returning 0.0 for them instead. The exact thresholds for this to occur depend on F.

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>,