rand_distr

Struct Poisson

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

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.

Poisson distribution

§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.

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impl<F> Poisson<F>

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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.

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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.

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impl<F> Clone for Poisson<F>

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

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl<F> Debug for Poisson<F>

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

Formats the value using the given formatter. Read more
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impl<'de, F> Deserialize<'de> for Poisson<F>

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fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>
where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer. Read more
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impl<F> Distribution<F> for Poisson<F>

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

Generate a random value of T, using rng as the source of randomness.
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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. Read more
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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 Read more
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impl<F> PartialEq for Poisson<F>

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

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<F> Serialize for Poisson<F>

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

Serialize this value into the given Serde serializer. Read more
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impl<F> Copy for Poisson<F>

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impl<F> StructuralPartialEq for Poisson<F>

Auto Trait Implementations§

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impl<F> Freeze for Poisson<F>
where F: Freeze,

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impl<F> RefUnwindSafe for Poisson<F>
where F: RefUnwindSafe,

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impl<F> Send for Poisson<F>
where F: Send,

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impl<F> Sync for Poisson<F>
where F: Sync,

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impl<F> Unpin for Poisson<F>
where F: Unpin,

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impl<F> UnwindSafe for Poisson<F>
where F: UnwindSafe,

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dst: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dst. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<V, T> VZip<V> for T
where V: MultiLane<T>,

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fn vzip(self) -> V

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impl<T> DeserializeOwned for T
where T: for<'de> Deserialize<'de>,