Struct Cauchy

pub struct Cauchy { /* private fields */ }

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().unwrap(), 0.0);
assert_eq!(n.pdf(1.0), 0.1591549430918953357689);

Implementations

impl Cauchy

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

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());

pub 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);

pub 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 Clone for Cauchy

fn clone(&self) -> Cauchy

Returns a duplicate of the value.

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

Performs copy-assignment from source.

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

impl ContinuousCDF<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

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

Calculates the survival 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. note that this is identical to the cdf except for the negative argument to the arctan function

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

Calculates the inverse cumulative distribution function for the cauchy distribution at x

Formula

x_0 + γ tan((x - 0.5) π)

where x_0 is the location and γ is the scale

impl Debug for Cauchy

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

Formats the value using the given formatter.

impl Display for Cauchy

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

Formats the value using the given formatter.

impl Distribution<f64> for Cauchy

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

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 Distribution<f64> for Cauchy

fn entropy(&self) -> Option<f64>

Returns the entropy of the cauchy distribution

Formula

ln(γ) + ln(4π)

where γ is the scale

fn mean(&self) -> Option<T>

Returns the mean, if it exists.

fn variance(&self) -> Option<T>

Returns the variance, if it exists.

fn std_dev(&self) -> Option<T>

Returns the standard deviation, if it exists.

fn skewness(&self) -> Option<T>

Returns the skewness, if it exists.

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

f64::INFINITY

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 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 Mode<Option<f64>> for Cauchy

fn mode(&self) -> Option<f64>

Returns the mode of the cauchy distribution

Formula

x_0

where x_0 is the location

impl PartialEq for Cauchy

fn eq(&self, other: &Cauchy) -> 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 Copy for Cauchy

impl StructuralPartialEq for Cauchy