Struct statrs::distribution::Chi

pub struct Chi { /* fields omitted */ }

Implements the Chi distribution

Examples

use statrs::distribution::{Chi, Continuous};
use statrs::statistics::Mean;
use statrs::prec;

let n = Chi::new(2.0).unwrap();
assert!(prec::almost_eq(n.mean(), 1.25331413731550025121, 1e-14));
assert!(prec::almost_eq(n.pdf(1.0), 0.60653065971263342360, 1e-15));

Methods

impl Chi

pub fn new(freedom: f64) -> Result<Chi>

Constructs a new chi distribution with freedom degrees of freedom

Errors

Returns an error if freedom is NaN or less than or equal to 0.0

Examples

use statrs::distribution::Chi;

let mut result = Chi::new(2.0);
assert!(result.is_ok());

result = Chi::new(0.0);
assert!(result.is_err());

pub fn freedom(&self) -> f64

Returns the degrees of freedom of the chi distribution.

Examples

use statrs::distribution::Chi;

let n = Chi::new(2.0).unwrap();
assert_eq!(n.freedom(), 2.0);

Trait Implementations

impl Univariate<f64, f64> for Chi

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

Calculates the cumulative distribution function for the chi distribution at x.

Formula

P(k / 2, x^2 / 2)

where k is the degrees of freedom and P is the regularized Gamma function

impl Continuous<f64, f64> for Chi

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

Calculates the probability density function for the chi distribution at x

Formula

(2^(1 - (k / 2)) * x^(k - 1) * e^(-x^2 / 2)) / Γ(k / 2)

where k is the degrees of freedom and Γ is the gamma function

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

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

Formula

ln((2^(1 - (k / 2)) * x^(k - 1) * e^(-x^2 / 2)) / Γ(k / 2))

impl Min<f64> for Chi

fn min(&self) -> f64

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

Formula

0

impl Max<f64> for Chi

fn max(&self) -> f64

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

Formula

INF

impl Mean<f64> for Chi

fn mean(&self) -> f64

Returns the mean of the chi distribution

Remarks

Returns NaN if freedom is INF

Formula

sqrt2 * Γ((k + 1) / 2) / Γ(k / 2)

where k is degrees of freedom and Γ is the gamma function

impl Variance<f64> for Chi

fn variance(&self) -> f64

Returns the variance of the chi distribution

Remarks

Returns NaN if freedom is INF

Formula

k - μ^2

where k is degrees of freedom and μ is the mean of the distribution

fn std_dev(&self) -> f64

Returns the standard deviation of the chi distribution

Remarks

Returns NaN if freedom is INF

Formula

sqrt(k - μ^2)

where k is degrees of freedom and μ is the mean of the distribution

impl Entropy<f64> for Chi

fn entropy(&self) -> f64

Returns the entropy of the chi distribution

Remarks

Returns NaN if freedom is INF

Formula

ln(Γ(k / 2)) + 0.5 * (k - ln2 - (k - 1) * ψ(k / 2))

where k is degrees of freedom, Γ is the gamma function, and ψ is the digamma function

impl Skewness<f64> for Chi

fn skewness(&self) -> f64

Returns the skewness of the chi distribution

Remarks

Returns NaN if freedom is INF

Formula

(μ / σ^3) * (1 - 2σ^2)

where μ is the mean and σ the standard deviation of the distribution

impl Mode<f64> for Chi

fn mode(&self) -> f64

Returns the mode for the chi distribution

Panics

If freedom < 1.0

Formula

sqrt(k - 1)

where k is the degrees of freedom

impl CheckedMode<f64> for Chi

fn checked_mode(&self) -> Result<f64>

Returns the mode for the chi distribution

Errors

If freedom < 1.0

Formula

sqrt(k - 1)

where k is the degrees of freedom

impl Copy for Chi

impl PartialEq<Chi> for Chi

fn eq(&self, other: &Chi) -> bool

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

fn ne(&self, other: &Chi) -> bool

This method tests for !=.

impl Clone for Chi

fn clone(&self) -> Chi

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Chi

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

Formats the value using the given formatter.

impl Distribution<f64> for Chi

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>(&'a self, rng: &'a mut R) -> DistIter<'a, Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.