Struct probability::distribution::Cauchy

pub struct Cauchy { /* private fields */ }

A Cauchy distribution.

The Cauchy distribution (also known as Lorentz or Cauchy–Lorentz distribution) is a continuous probability distribution with a location parameter x_0, a scale parameter gamma > 0, and the following probability density function:

p(x) = 1 / (pi * gamma * (1 + ((x - x_0) / gamma)^2)).

The distribution is long tailed and has no mean or variance. It is unimodal with the mode at x_0, around which it is symmetric.

Implementations

impl Cauchy

pub fn new(x_0: f64, gamma: f64) -> Self

Create a Cauchy distribution with location x_0 and scale gamma.

It should hold that gamma > 0.

pub fn x_0(&self) -> f64

Return the location parameter.

pub fn gamma(&self) -> f64

Return the scale parameter.

Trait Implementations

impl Clone for Cauchy

fn clone(&self) -> Cauchy

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Continuous for Cauchy

fn density(&self, x: f64) -> f64

Compute the probability density function.

impl Debug for Cauchy

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

Formats the value using the given formatter.

impl Distribution for Cauchy

type Value = f64

The type of outcomes.

fn distribution(&self, x: f64) -> f64

Compute the cumulative distribution function.

impl Entropy for Cauchy

fn entropy(&self) -> f64

Compute the differential entropy.

impl Inverse for Cauchy

fn inverse(&self, p: f64) -> f64

Compute the inverse of the cumulative distribution function.

impl Median for Cauchy

fn median(&self) -> f64

Compute the median.

impl Modes for Cauchy

fn modes(&self) -> Vec<f64>

Compute the modes.

impl Sample for Cauchy

fn sample<S>(&self, source: &mut S) -> f64where
    S: Source,

Draw a sample.

impl Copy for Cauchy