Struct Beta 

pub struct Beta { /* private fields */ }

A continuous distribution on the interval (0, 1), commonly used for modeling probabilities and proportions.

Conjugate prior for Bernoulli/Binomial distributions.

Mathematical Properties:

• Support: (0, 1); the closed endpoints 0 and 1 are handled as limits
• PDF: f(x) = (x^(α-1) × (1-x)^(β-1)) / B(α,β)
• Mean: α / (α + β)
• Variance: (αβ) / ((α+β)²(α+β+1))

Boundary semantics (matching scipy.stats.beta.logpdf): at x = 0, log_prob is -∞ when α > 1 (density → 0), ln(β) when α == 1, and +∞ when α < 1 (density diverges, e.g. the Jeffreys prior Beta(0.5, 0.5)). The endpoint x = 1 is symmetric in β.

Example:

// Uniform on [0,1]
let uniform = sample(addr!("p"), Beta::new(1.0, 1.0).unwrap());

// Prior for success probability
let prob_prior = sample(addr!("success_rate"), Beta::new(2.0, 5.0).unwrap());

// Conjugate prior-likelihood pair
let model = sample(addr!("p"), Beta::new(3.0, 7.0).unwrap())
    .bind(|p| observe(addr!("trial"), Bernoulli::new(p).unwrap(), true));

// Skewed towards 0 (beta > alpha)
let skewed = sample(addr!("proportion"), Beta::new(2.0, 8.0).unwrap());

Implementations

impl Beta

pub fn new(alpha: f64, beta: f64) -> FugueResult<Self>

Create a new Beta distribution with validated parameters.

pub fn uniform_prior() -> Self

Create the uniform-prior Beta distribution Beta(1, 1).

FG-29: infallible constructor for the statically-valid α = β = 1 case, which is exactly the uniform distribution on (0, 1) and the standard uninformative conjugate prior for a Bernoulli/Binomial probability; avoids new(1.0, 1.0).unwrap().

let prior = Beta::uniform_prior();
assert_eq!(prior.alpha(), 1.0);
assert_eq!(prior.beta(), 1.0);

pub fn alpha(&self) -> f64

Get the alpha parameter.

pub fn beta(&self) -> f64

Get the beta parameter.

Trait Implementations

impl Clone for Beta

fn clone(&self) -> Beta

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Beta

impl Debug for Beta

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

Formats the value using the given formatter.

impl Distribution<f64> for Beta

fn sample(&self, rng: &mut dyn RngCore) -> f64

Generate a random sample (with its natural type), T, from the distribution, using the provided random number generator, rng.

fn log_prob(&self, x: &f64) -> LogF64

Compute the log-probability density (continuous) or mass (discrete) of a value, x, from the distribution.

fn clone_box(&self) -> Box<dyn Distribution<f64>>

Clone the distribution into a boxed trait object, Box<dyn Distribution<T>>.

impl Validate for Beta

fn validate(&self) -> FugueResult<()>