Struct Cauchy

pub struct Cauchy<F>
where
    F: Float + FloatConst,
    StandardUniform: Distribution<F>,
{ /* private fields */ }

The Cauchy distribution Cauchy(x₀, γ).

The Cauchy distribution is a continuous probability distribution with parameters x₀ (median) and γ (scale). It describes the distribution of the ratio of two independent normally distributed random variables with means x₀ and scales γ. In other words, if X and Y are independent normally distributed random variables with means x₀ and scales γ, respectively, then X / Y is Cauchy(x₀, γ) distributed.

Density function

f(x) = 1 / (π * γ * (1 + ((x - x₀) / γ)²))

Plot

The plot illustrates the Cauchy distribution with various values of x₀ and γ. Note how the median parameter x₀ shifts the distribution along the x-axis, and how the scale γ changes the density around the median.

The standard Cauchy distribution is the special case with x₀ = 0 and γ = 1, which corresponds to the ratio of two StandardNormal distributions.

Example

use rand_distr::{Cauchy, Distribution};

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

Notes

Note that at least for f32, results are not fully portable due to minor differences in the target system’s tan implementation, tanf.

Implementations

impl<F> Cauchy<F>

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

pub fn new(median: F, scale: F) -> Result<Cauchy<F>, Error>

Construct a new Cauchy with the given shape parameters median the peak location and scale the scale factor.

Trait Implementations

impl<F> Clone for Cauchy<F>

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

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<F> Debug for Cauchy<F>

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

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

Formats the value using the given formatter.

impl<F> Distribution<F> for Cauchy<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) -> 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 Cauchy<F>

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

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

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

impl<F> StructuralPartialEq for Cauchy<F>

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