Struct Chi

pub struct Chi { /* private fields */ }

Implements the Chi distribution

Examples

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

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

Implementations

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 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 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 ContinuousCDF<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 lower incomplete Gamma function

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

Calculates the survival 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 upper incomplete Gamma function

fn inverse_cdf(&self, p: T) -> K

Due to issues with rounding and floating-point accuracy the default implementation may be ill-behaved. Specialized inverse cdfs should be used whenever possible. Performs a binary search on the domain of cdf to obtain an approximation of F^-1(p) := inf { x | F(x) >= p }. Needless to say, performance may may be lacking.

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, rng: &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 Chi

fn mean(&self) -> Option<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

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

Returns the entropy of the chi distribution

Remarks

Returns None 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

fn skewness(&self) -> Option<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

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

Returns the standard deviation, if it exists.

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 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 Mode<Option<f64>> for Chi

fn mode(&self) -> Option<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 PartialEq for Chi

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

impl StructuralPartialEq for Chi