Struct statrs::distribution::Cauchy

pub struct Cauchy { /* fields omitted */ }

Implements the Cauchy distribution, also known as the Lorentz distribution.

Examples

use statrs::distribution::{Cauchy, Continuous};
use statrs::statistics::Mode;

let n = Cauchy::new(0.0, 1.0).unwrap();
assert_eq!(n.mode(), 0.0);
assert_eq!(n.pdf(1.0), 0.1591549430918953357689);

Methods

impl Cauchy

fn new(location: f64, scale: f64) -> Result<Cauchy>

Constructs a new cauchy distribution with the given location and scale.

Errors

Returns an error if location or scale are NaN or scale <= 0.0

Examples

use statrs::distribution::Cauchy;

let mut result = Cauchy::new(0.0, 1.0);
assert!(result.is_ok());

result = Cauchy::new(0.0, -1.0);
assert!(result.is_err());

fn location(&self) -> f64

Returns the location of the cauchy distribution

Examples

use statrs::distribution::Cauchy;

let n = Cauchy::new(0.0, 1.0).unwrap();
assert_eq!(n.location(), 0.0);

fn scale(&self) -> f64

Returns the scale of the cauchy distribution

Examples

use statrs::distribution::Cauchy;

let n = Cauchy::new(0.0, 1.0).unwrap();
assert_eq!(n.scale(), 1.0);

Trait Implementations

impl Debug for Cauchy

fn fmt(&self, __arg_0: &mut Formatter) -> Result

Formats the value using the given formatter.

impl Copy for Cauchy

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 PartialEq for Cauchy

fn eq(&self, __arg_0: &Cauchy) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, __arg_0: &Cauchy) -> bool

This method tests for !=.

impl Sample<f64> for Cauchy

fn sample<R: Rng>(&mut self, r: &mut R) -> f64

Generate a random sample from a cauchy distribution using r as the source of randomness. Refer here for implementation details

impl IndependentSample<f64> for Cauchy

fn ind_sample<R: Rng>(&self, r: &mut R) -> f64

Generate a random independent sample from a cauchy distribution using r as the source of randomness. Refer here for implementation details

impl Distribution<f64> for Cauchy

fn sample<R: Rng>(&self, r: &mut R) -> f64

Generate a random sample from the cauchy distribution using r as the source of randomness

Examples

use rand::StdRng;
use statrs::distribution::{Cauchy, Distribution};

let mut r = rand::StdRng::new().unwrap();
let n = Cauchy::new(0.0, 1.0).unwrap();
print!("{}", n.sample::<StdRng>(&mut r));

impl Univariate<f64, f64> for Cauchy

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

Calculates the cumulative distribution function for the cauchy distribution at x

Formula

(1 / π) * arctan((x - x_0) / γ) + 0.5

where x_0 is the location and γ is the scale

impl Min<f64> for Cauchy

fn min(&self) -> f64

Returns the minimum value in the domain of the cauchy distribution representable by a double precision float

Formula

NEG_INF

impl Max<f64> for Cauchy

fn max(&self) -> f64

Returns the maximum value in the domain of the cauchy distribution representable by a double precision float

Formula

INF

impl Entropy<f64> for Cauchy

fn entropy(&self) -> f64

Returns the entropy of the cauchy distribution

Formula

ln(γ) + ln(4π)

where γ is the scale

impl Median<f64> for Cauchy

fn median(&self) -> f64

Returns the median of the cauchy distribution

Formula

x_0

where x_0 is the location

impl Mode<f64> for Cauchy

fn mode(&self) -> f64

Returns the mode of the cauchy distribution

Formula

x_0

where x_0 is the location

impl Continuous<f64, f64> for Cauchy

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

Calculates the probability density function for the cauchy distribution at x

Formula

1 / (πγ * (1 + ((x - x_0) / γ)^2))

where x_0 is the location and γ is the scale

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

Calculates the log probability density function for the cauchy distribution at x

Formula

ln(1 / (πγ * (1 + ((x - x_0) / γ)^2)))

where x_0 is the location and γ is the scale