Struct Gumbel

pub struct Gumbel<F>
where
    F: Float,
    OpenClosed01: Distribution<F>,
{ /* private fields */ }

The Gumbel distribution Gumbel(μ, β).

The Gumbel distribution is a continuous probability distribution with location parameter μ (mu) and scale parameter β (beta). It is used to model the distribution of the maximum (or minimum) of a number of samples of various distributions.

Density function

f(x) = exp(-(z + exp(-z))) / β, where z = (x - μ) / β.

Plot

The following plot illustrates the Gumbel distribution with various values of μ and β. Note how the location parameter μ shifts the distribution along the x-axis, and the scale parameter β changes the density around μ. Note also the asymptotic behavior of the distribution towards the right.

Example

use rand::prelude::*;
use rand_distr::Gumbel;

let val: f64 = rand::rng().sample(Gumbel::new(0.0, 1.0).unwrap());
println!("{}", val);

Implementations

impl<F> Gumbel<F>

where F: Float, OpenClosed01: Distribution<F>,

pub fn new(location: F, scale: F) -> Result<Gumbel<F>, Error>

Construct a new Gumbel distribution with given location and scale.

Trait Implementations

impl<F> Clone for Gumbel<F>

where F: Float + Clone, OpenClosed01: Distribution<F>,

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<F> Debug for Gumbel<F>

where F: Float + Debug, OpenClosed01: Distribution<F>,

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

Formats the value using the given formatter.

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

where F: Float + Deserialize<'de>, OpenClosed01: 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 Gumbel<F>

where F: Float, OpenClosed01: 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 Gumbel<F>

where F: Float + PartialEq, OpenClosed01: Distribution<F>,

fn eq(&self, other: &Gumbel<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 Gumbel<F>

where F: Float + Serialize, OpenClosed01: 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 Gumbel<F>

where F: Float + Copy, OpenClosed01: Distribution<F>,

impl<F> StructuralPartialEq for Gumbel<F>

where F: Float, OpenClosed01: Distribution<F>,