Implementation:Avhz RustQuant Distribution Trait

Knowledge Sources	RustQuant
Domains	Mathematics, Statistics
Last Updated	2026-02-07 19:00 GMT

Overview

Concrete trait definition for all probability distributions provided by the RustQuant library.

Description

The Distribution trait is the base trait that all probability distributions in RustQuant must implement. It defines a unified interface for working with any probability distribution, ensuring consistent access to density functions, statistical moments, and random sampling.

The module also defines:

• DistributionClass -- an enum with variants Discrete and Continuous, used by distributions that support both forms (such as the Uniform distribution).
• i -- a convenience constant for the imaginary unit as a Complex<f64>.

The trait requires 14 methods:

• cf(t) -- Characteristic function, E[e^{itX}], returning a Complex<f64>.
• pdf(x) -- Probability density function (panics if the distribution is discrete).
• pmf(x) -- Probability mass function (panics if the distribution is continuous).
• cdf(x) -- Cumulative distribution function, P(X <= x).
• inv_cdf(p) -- Inverse CDF (quantile function), the value x such that cdf(x) = p.
• mean() -- Expected value.
• median() -- Median value.
• mode() -- Most likely value.
• variance() -- Variance, a measure of spread.
• skewness() -- Skewness, a measure of asymmetry.
• kurtosis() -- Kurtosis, a measure of tail heaviness.
• entropy() -- Shannon entropy.
• mgf(t) -- Moment generating function, E[e^{tX}].
• sample(n) -- Generate n random samples, returning Result<Vec<f64>, RustQuantError>.

Usage

Implement this trait on any new probability distribution struct to integrate it into the RustQuant distribution framework. Use the trait as a bound in generic functions that need to work with any distribution type (e.g., computing moments, generating samples, or evaluating density functions polymorphically).

Code Reference

Source Location

• Repository: RustQuant
• File: crates/RustQuant_math/src/distributions/distribution.rs
• Lines: 1-95

Signature

pub const i: Complex<f64> = Complex { re: 0.0, im: 1.0 };

pub enum DistributionClass {
    Discrete,
    Continuous,
}

pub trait Distribution {
    fn cf(&self, t: f64) -> Complex<f64>;
    fn pdf(&self, x: f64) -> f64;
    fn pmf(&self, x: f64) -> f64;
    fn cdf(&self, x: f64) -> f64;
    fn inv_cdf(&self, p: f64) -> f64;
    fn mean(&self) -> f64;
    fn median(&self) -> f64;
    fn mode(&self) -> f64;
    fn variance(&self) -> f64;
    fn skewness(&self) -> f64;
    fn kurtosis(&self) -> f64;
    fn entropy(&self) -> f64;
    fn mgf(&self, t: f64) -> f64;
    fn sample(&self, n: usize) -> Result<Vec<f64>, RustQuantError>;
}

Import

use RustQuant::math::distributions::Distribution;
use RustQuant::math::distributions::DistributionClass;

I/O Contract

Inputs

Name	Type	Required	Description
t	f64	Yes (for cf, mgf)	Evaluation point for characteristic/moment generating functions.
x	f64	Yes (for pdf, pmf, cdf)	Evaluation point for density/mass/distribution functions.
p	f64	Yes (for inv_cdf)	Probability value for the quantile function. Must be in [0, 1].
n	usize	Yes (for sample)	Number of random samples to generate.

Outputs

Name	Type	Description
cf()	Complex<f64>	Value of the characteristic function at t.
pdf() / pmf()	f64	Probability density or mass at x.
cdf()	f64	Cumulative probability up to x.
inv_cdf()	f64	Quantile value for given probability p.
mean(), median(), mode()	f64	Location summary statistics.
variance(), skewness(), kurtosis()	f64	Shape summary statistics.
entropy()	f64	Shannon entropy of the distribution.
mgf()	f64	Value of the moment generating function at t.
sample()	Result<Vec<f64>, RustQuantError>	Vector of random variates.

Usage Examples

use RustQuant::math::distributions::{Distribution, Gaussian};

// Any struct implementing Distribution can be used generically
fn print_summary<D: Distribution>(dist: &D) {
    println!("Mean: {}", dist.mean());
    println!("Variance: {}", dist.variance());
    println!("Skewness: {}", dist.skewness());
    println!("Kurtosis: {}", dist.kurtosis());
}

let gaussian = Gaussian::new(0.0, 1.0);
print_summary(&gaussian);

// Generate samples from any distribution
let samples = gaussian.sample(1000).expect("sampled");

Related Pages

• Principle:Avhz_RustQuant_Probability_Distributions