Struct ChiSquared

pub struct ChiSquared { /* private fields */ }

Chi-Squared distribution: X ~ ChiSq(k)

Implementations

impl ChiSquared

pub fn new(k: usize) -> ChiSquared

New instance of a Chi-Squared distribution.

Examples

let dist = ChiSquared::new(1);

assert_eq!(dist.mean(), 1.0);

Panics

Panics if k is not positive.

Trait Implementations

impl Default for ChiSquared

fn default() -> ChiSquared

Returns the “default value” for a type.

impl Distribution for ChiSquared

fn cf(&self, t: f64) -> Complex<f64>

Characteristic function of the Chi-Squared distribution.

Examples

let chi = ChiSquared::new(1);
let cf = chi.cf(1.0);

assert_approx_equal!(cf.re, 0.5688645, 1e-7);
assert_approx_equal!(cf.im, 0.3515776, 1e-7);

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

Probability density function of the Chi-Squared distribution.

Examples

let chi = ChiSquared::new(1);

assert_approx_equal!(chi.pdf(1.0), 0.2419707, 1e-7);

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

Probability mass function of the Chi-Squared distribution. Using this method will call self.pdf(x) instead

Examples

let chi = ChiSquared::new(1);

assert_approx_equal!(chi.pmf(1.0), 0.2419707, 1e-7);
assert_approx_equal!(chi.pmf(1.0), chi.pdf(1.0), 1e-7);

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

Cumulative distribution function of the Chi-Squared distribution.

Examples

let chi = ChiSquared::new(1);

assert_approx_equal!(chi.cdf(1.0), 0.6826895, 1e-7);

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

Inverse (quantile) distribution function of the Chi-Squared distribution.

Examples

let chi = ChiSquared::new(1);

assert_approx_equal!(chi.inv_cdf(0.6826895), 1.0, 1e-7);

fn mean(&self) -> f64

Mean of the Chi-Squared distribution.

Examples

let chi = ChiSquared::new(1);

assert_eq!(chi.mean(), 1.0);

fn median(&self) -> f64

Median of the Chi-Squared distribution.

Examples

let chi = ChiSquared::new(1);

assert_approx_equal!(chi.median(), 0.4705075, 1e-7);

fn mode(&self) -> f64

Mode of the Chi-Squared distribution.

Examples

let chi = ChiSquared::new(1);

assert_eq!(chi.mode(), 0.0);

fn variance(&self) -> f64

Variance of the Chi-Squared distribution.

Examples

let chi = ChiSquared::new(1);

assert_eq!(chi.variance(), 2.0);

fn skewness(&self) -> f64

Skewness of the Chi-Squared distribution.

Examples

let chi = ChiSquared::new(1);

assert_approx_equal!(chi.skewness(), 2.8284271, 1e-7);

fn kurtosis(&self) -> f64

Kurtosis of the Chi-Squared distribution.

Examples

let chi = ChiSquared::new(1);

assert_eq!(chi.kurtosis(), 12.0);

fn entropy(&self) -> f64

Entropy of the Chi-Squared distribution.

Examples

let chi = ChiSquared::new(1);

assert_approx_equal!(chi.entropy(), 0.7837571, 1e-7);

fn mgf(&self, t: f64) -> f64

Moment-generating function of the Chi-Squared distribution.

Examples

let chi = ChiSquared::new(1);

assert_approx_equal!(chi.mgf(0.25), 1.4142135, 1e-7);

fn sample(&self, n: usize) -> Result<Vec<f64>, RustQuantError>

Generates a random sample from a Chi-Squared distribution.

Examples

let chi = ChiSquared::new(100);

let sample = chi.sample(100).expect("Error generating Chi-Squared sample.");
let mean = sample.iter().sum::<f64>() / sample.len() as f64;

assert_approx_equal!(mean, chi.mean(), 5.0);