Struct Poisson

pub struct Poisson<F>(/* private fields */)
where
    F: Float + FloatConst,
    StandardUniform: Distribution<F>;

The Poisson distribution Poisson(λ).

The Poisson distribution is a discrete probability distribution with rate parameter λ (lambda). It models the number of events occurring in a fixed interval of time or space.

This distribution has density function: f(k) = λ^k * exp(-λ) / k! for k >= 0.

Plot

The following plot shows the Poisson distribution with various values of λ. Note how the expected number of events increases with λ.

Example

use rand_distr::{Poisson, Distribution};

let poi = Poisson::new(2.0).unwrap();
let v: f64 = poi.sample(&mut rand::rng());
println!("{} is from a Poisson(2) distribution", v);

Integer vs FP return type

This implementation uses floating-point (FP) logic internally.

Due to the parameter limit λ < Self::MAX_LAMBDA, it statistically impossible to sample a value larger u64::MAX. As such, it is reasonable to cast generated samples to u64 using as: distr.sample(&mut rng) as u64 (and memory safe since Rust 1.45). Similarly, when λ < 4.2e9 it can be safely assumed that samples are less than u32::MAX.

Implementations

impl<F> Poisson<F>

where F: Float + FloatConst, StandardUniform: Distribution<F>,

pub const MAX_LAMBDA: f64 = 1.844E+19f64

The maximum supported value of lambda

This value was selected such that MAX_LAMBDA + 1e6 * sqrt(MAX_LAMBDA) < 2^64 - 1, thus ensuring that the probability of sampling a value larger than u64::MAX is less than 1e-1000.

Applying this limit also solves #1312.

pub fn new(lambda: F) -> Result<Poisson<F>, Error>

Construct a new Poisson with the given shape parameter lambda.

The maximum allowed lambda is MAX_LAMBDA.

Trait Implementations

impl<F> Clone for Poisson<F>

where F: Float + FloatConst + Clone, StandardUniform: Distribution<F>,

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<F> Debug for Poisson<F>

where F: Float + FloatConst + Debug, StandardUniform: Distribution<F>,

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

Formats the value using the given formatter.

impl<'de, F> Deserialize<'de> for Poisson<F>

where F: Float + FloatConst + Deserialize<'de>, StandardUniform: Distribution<F>,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<F> Distribution<F> for Poisson<F>

where F: Float + FloatConst, StandardUniform: Distribution<F>,

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

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, 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) -> DistMap<Self, F, T, S>

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

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<F> PartialEq for Poisson<F>

where F: Float + FloatConst + PartialEq, StandardUniform: Distribution<F>,

fn eq(&self, other: &Poisson<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> Serialize for Poisson<F>

where F: Float + FloatConst + Serialize, StandardUniform: Distribution<F>,

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<F> Copy for Poisson<F>

where F: Float + FloatConst + Copy, StandardUniform: Distribution<F>,

impl<F> StructuralPartialEq for Poisson<F>

where F: Float + FloatConst, StandardUniform: Distribution<F>,