Implementation:Avhz RustQuant Bernoulli Distribution
| Knowledge Sources | |
|---|---|
| Domains | Mathematics, Statistics |
| Last Updated | 2026-02-07 19:00 GMT |
Overview
Concrete implementation of the Bernoulli probability distribution provided by the RustQuant library.
Description
The Bernoulli struct models the Bernoulli distribution, denoted X ~ Bern(p). This is a discrete probability distribution that takes the value 1 with probability p and the value 0 with probability q = 1 - p. It is the simplest discrete distribution and serves as a building block for the Binomial distribution.
The struct contains a single field:
- p (f64) -- the probability of success (k = 1), constrained to [0, 1].
The implementation provides the full Distribution trait interface including: characteristic function (cf), probability mass function (pmf), cumulative distribution function (cdf), inverse CDF (quantile function), statistical moments (mean, median, mode, variance, skewness, kurtosis), entropy, moment generating function (mgf), and random sampling. A Default implementation sets p = 0.5.
The pdf method delegates to pmf since the Bernoulli distribution is discrete. Random sampling is performed using the rand_distr crate internally.
Usage
Use this distribution when modeling binary outcomes (success/failure, yes/no, true/false) with a fixed probability of success. Common applications in quantitative finance include modeling default/no-default events, barrier breaches, and binary option payoffs.
Code Reference
Source Location
- Repository: RustQuant
- File: crates/RustQuant_math/src/distributions/bernoulli.rs
- Lines: 1-464
Signature
pub struct Bernoulli {
p: f64,
}
impl Bernoulli {
pub fn new(probability: f64) -> Bernoulli
}
impl Distribution for Bernoulli {
fn cf(&self, t: f64) -> Complex<f64>;
fn pdf(&self, x: f64) -> f64;
fn pmf(&self, k: f64) -> f64;
fn cdf(&self, k: 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::Bernoulli;
use RustQuant::math::distributions::Distribution;
I/O Contract
Inputs
| Name | Type | Required | Description |
|---|---|---|---|
| probability | f64 | Yes | Probability of success (k = 1). Must be in [0, 1]. |
Outputs
| Name | Type | Description |
|---|---|---|
| Bernoulli | struct | A new Bernoulli distribution instance with the given probability. |
| mean() | f64 | Returns p. |
| variance() | f64 | Returns p * (1 - p). |
| sample(n) | Result<Vec<f64>, RustQuantError> | A vector of n random variates, each 0.0 or 1.0. |
Usage Examples
use RustQuant::math::distributions::{Bernoulli, Distribution};
// Create a Bernoulli distribution with p = 0.5
let bernoulli = Bernoulli::new(0.5);
// Statistical moments
assert_eq!(bernoulli.mean(), 0.5);
assert_eq!(bernoulli.variance(), 0.25);
assert_eq!(bernoulli.skewness(), 0.0);
assert_eq!(bernoulli.kurtosis(), -2.0);
// Probability mass function
assert_eq!(bernoulli.pmf(1.0), 0.5);
assert_eq!(bernoulli.pmf(0.0), 0.5);
// Cumulative distribution function
assert_eq!(bernoulli.cdf(0.0), 0.5);
assert_eq!(bernoulli.cdf(1.0), 1.0);
// Generate 100 random samples
let sample = bernoulli.sample(100).expect("Bernoulli sampled.");