Struct ChiSquared 

pub struct ChiSquared {
    pub k: f64,
}

Chi-squared distribution with k degrees of freedom.

The chi-squared distribution is a special case of the Gamma distribution with shape = k/2 and rate = 1/2.

Mathematical Definition

• PDF: f(x) = x^(k/2−1) exp(−x/2) / (2^(k/2) Γ(k/2))
• CDF: F(x) = P(k/2, x/2) (regularized lower incomplete gamma)
• Mean: k
• Variance: 2k

Examples

use u_numflow::distributions::ChiSquared;

let chi2 = ChiSquared::new(3.0).unwrap();
assert!((chi2.mean() - 3.0).abs() < 1e-10);
assert!((chi2.variance() - 6.0).abs() < 1e-10);
assert!((chi2.cdf(0.0)).abs() < 1e-10);

References

Johnson, N. L., Kotz, S., & Balakrishnan, N. (1994). Continuous Univariate Distributions, Vol. 1, Chapter 18.

Fields

k: f64

Degrees of freedom k > 0.

Implementations

impl ChiSquared

pub fn new(k: f64) -> Result<Self, DistributionError>

Creates a new Chi-squared distribution with k degrees of freedom.

Errors

Returns DistributionError if k ≤ 0.

pub fn mean(&self) -> f64

Returns the mean: k.

pub fn variance(&self) -> f64

Returns the variance: 2k.

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

Evaluates the PDF at x.

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

Evaluates the CDF at x: F(x) = P(k/2, x/2).

pub fn quantile(&self, p: f64) -> Option<f64>

Evaluates the quantile (inverse CDF) at probability p ∈ [0, 1].

Delegates to Gamma(k/2, 1/2) quantile since Chi2(k) = Gamma(k/2, 1/2).

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 Debug for ChiSquared

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

Formats the value using the given formatter.