Struct Beta 

pub struct Beta { /* private fields */ }

Β distribution with shape parameters a > 0 and b > 0.

Defined over the interval [0 . . 1], with density f(x; a, b) = xᵃ ⁻ ¹ (1 − x)ᵇ ⁻ ¹ / Β(a, b).

Example

use cdflib::Beta;
use cdflib::traits::ContinuousCdf;

let b = Beta::new(2.0, 5.0);

// Pr[X ≤ 0.3]
let p = b.cdf(0.3);

// Compute parameter a given Pr[X ≤ 0.5] = 0.9 and b = 2.0
let a = Beta::search_a(0.9, 0.1, 0.5, 2.0).unwrap();

Implementations

impl Beta

pub fn new(a: f64, b: f64) -> Self

Construct a Β(a, b) distribution with the given shape parameters.

Panics

Panics if either parameter is invalid; use try_new for a fallible variant.

pub fn try_new(a: f64, b: f64) -> Result<Self, BetaError>

Fallible counterpart of new returning a BetaError instead of panicking.

Returns ANotPositive, ANotFinite, BNotPositive, or BNotFinite if either parameter fails its validity check.

pub const fn a(&self) -> f64

Returns the shape parameter a.

pub const fn b(&self) -> f64

Returns the shape parameter b.

pub fn search_a(p: f64, q: f64, x: f64, b: f64) -> Result<f64, BetaError>

Returns the shape parameter a satisfying Pr[X ≤ x] = p.

CDFLIB’s cdfbet with which = 3. Caller passes both p and q = 1 − p; consistency is enforced within 3 ε.

pub fn search_b(p: f64, q: f64, x: f64, a: f64) -> Result<f64, BetaError>

Returns the shape parameter b satisfying Pr[X ≤ x] = p.

CDFLIB’s cdfbet with which = 4. Caller passes both p and q = 1 − p; consistency is enforced within 3 ε.

impl Beta

pub fn inverse_ccdf(&self, q: f64) -> Result<f64, BetaError>

Returns the quantile x such that ccdf(x) = q.

Mirrors CDFLIB’s cdfbet with which = 2, using the same cum - p / ccum - q pivot as the Fortran routine.

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 Continuous for Beta

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

Returns the density f(x) of the distribution at x.

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

Returns the logarithm of the density f(x). Computing in log-space avoids underflow in the tails.

impl ContinuousCdf for Beta

type Error = BetaError

Domain-specific error type returned by the inverse routines.

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

Returns Pr[X ≤ x].

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

Returns Pr[X > x], the complementary CDF.

fn inverse_cdf(&self, p: f64) -> Result<f64, BetaError>

Returns the smallest x such that cdf(x) ≥ p, for p ∈ [0 . . 1].

impl Debug for Beta

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

Formats the value using the given formatter.

impl Entropy for Beta

fn entropy(&self) -> f64

Returns the entropy of the distribution in nats.

impl Mean for Beta

fn mean(&self) -> f64

Returns the expected value E[X].

impl PartialEq for Beta

fn eq(&self, other: &Beta) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Variance for Beta

fn variance(&self) -> f64

Returns the variance Var(X) = E[(X − E[X])²].

fn std_dev(&self) -> f64

Returns the standard deviation (the square root of the variance).

impl Copy for Beta

impl StructuralPartialEq for Beta