Struct ChiSquared 

pub struct ChiSquared { /* private fields */ }

Implements the Chi-squared distribution which is a special case of the Gamma distribution (referenced Here)

Examples

use statrs::distribution::{ChiSquared, Continuous};
use statrs::statistics::Distribution;
use approx::assert_abs_diff_eq;

let n = ChiSquared::new(3.0).unwrap();
assert_eq!(n.mean().unwrap(), 3.0);
assert_abs_diff_eq!(n.pdf(4.0), 0.107981933026376103901, epsilon = 1e-15);

Implementations

impl ChiSquared

pub fn new(freedom: f64) -> Result<ChiSquared, GammaError>

Constructs a new chi-squared distribution with freedom degrees of freedom. This is equivalent to a Gamma distribution with a shape of freedom / 2.0 and a rate of 0.5.

Errors

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

Examples

use statrs::distribution::ChiSquared;

let mut result = ChiSquared::new(3.0);
assert!(result.is_ok());

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

pub fn freedom(&self) -> f64

Returns the degrees of freedom of the chi-squared distribution

Examples

use statrs::distribution::ChiSquared;

let n = ChiSquared::new(3.0).unwrap();
assert_eq!(n.freedom(), 3.0);

pub fn shape(&self) -> f64

Returns the shape of the underlying Gamma distribution

Examples

use statrs::distribution::ChiSquared;

let n = ChiSquared::new(3.0).unwrap();
assert_eq!(n.shape(), 3.0 / 2.0);

pub fn rate(&self) -> f64

Returns the rate of the underlying Gamma distribution

Examples

use statrs::distribution::ChiSquared;

let n = ChiSquared::new(3.0).unwrap();
assert_eq!(n.rate(), 0.5);

Trait Implementations

impl Clone for ChiSquared

fn clone(&self) -> ChiSquared

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Continuous<f64, f64> for ChiSquared

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

Calculates the probability density function for the chi-squared distribution at x

At x = 0, returns positive infinity for freedom < 2, 0.5 for freedom = 2, and 0 for freedom > 2.

Formula

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

At x = 0, returns positive infinity for freedom < 2, ln(0.5) for freedom = 2, and negative infinity for freedom > 2.

Formula

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

impl ContinuousCDF<f64, f64> for ChiSquared

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

Calculates the cumulative distribution function for the chi-squared distribution at x

Formula

(1 / Γ(k / 2)) * γ(k / 2, x / 2)

where k is the degrees of freedom, Γ is the gamma function, and γ is the lower incomplete gamma function

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

Calculates the cumulative distribution function for the chi-squared distribution at x

Formula

(1 / Γ(k / 2)) * γ(k / 2, x / 2)

where k is the degrees of freedom, Γ is the gamma function, and γ is the upper incomplete gamma function

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

Calculates the inverse cumulative distribution function for the chi-squared distribution at x

Formula

γ^{-1}(k / 2, x * Γ(k / 2) / 2)

where k is the degrees of freedom, Γ is the gamma function, and γ is the lower incomplete gamma function

fn try_inverse_cdf(&self, p: T) -> Result<K, InverseCdfError>

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 Copy for ChiSquared

impl Debug for ChiSquared

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

Formats the value using the given formatter.

impl Display for ChiSquared

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

Formats the value using the given formatter.

impl Distribution<f64> for ChiSquared

Available on crate feature rand only.

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) -> Iter<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) -> Map<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Map sampled values to type S

impl Distribution<f64> for ChiSquared

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

Returns the mean of the chi-squared distribution

Formula

k

where k is the degrees of freedom

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

Returns the variance of the chi-squared distribution

Formula

2k

where k is the degrees of freedom

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

Returns the entropy of the chi-squared distribution

Formula

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

where k is the 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-squared distribution

Formula

sqrt(8 / k)

where k is the degrees of freedom

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

Returns the standard deviation, if it exists.

impl Max<f64> for ChiSquared

fn max(&self) -> f64

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

Formula

f64::INFINITY

impl Median<f64> for ChiSquared

fn median(&self) -> f64

Returns the median of the chi-squared distribution

Formula

k * (1 - (2 / 9k))^3

impl Min<f64> for ChiSquared

fn min(&self) -> f64

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

Formula

0

impl Mode<Option<f64>> for ChiSquared

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

Returns the mode of the chi-squared distribution, or None if freedom is less than 2.

Formula

k - 2, where k >= 2

where k is the degrees of freedom

impl PartialEq for ChiSquared

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

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for ChiSquared