Struct statrs::distribution::Beta

pub struct Beta { /* private fields */ }

Implements the Beta distribution

Examples

use statrs::distribution::{Beta, Continuous};
use statrs::statistics::*;
use statrs::prec;

let n = Beta::new(2.0, 2.0).unwrap();
assert_eq!(n.mean().unwrap(), 0.5);
assert!(prec::almost_eq(n.pdf(0.5), 1.5, 1e-14));

Implementations

impl Beta

pub fn new(shape_a: f64, shape_b: f64) -> Result<Beta>

Constructs a new beta distribution with shapeA (α) of shape_a and shapeB (β) of shape_b

Errors

Returns an error if shape_a or shape_b are NaN. Also returns an error if shape_a <= 0.0 or shape_b <= 0.0

Examples

use statrs::distribution::Beta;

let mut result = Beta::new(2.0, 2.0);
assert!(result.is_ok());

result = Beta::new(0.0, 0.0);
assert!(result.is_err());

pub fn shape_a(&self) -> f64

Returns the shapeA (α) of the beta distribution

Examples

use statrs::distribution::Beta;

let n = Beta::new(2.0, 2.0).unwrap();
assert_eq!(n.shape_a(), 2.0);

pub fn shape_b(&self) -> f64

Returns the shapeB (β) of the beta distributionβ

Examples

use statrs::distribution::Beta;

let n = Beta::new(2.0, 2.0).unwrap();
assert_eq!(n.shape_b(), 2.0);

Trait Implementations

impl Clone for Beta

fn clone(&self) -> Beta

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Continuous<f64, f64> for Beta

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

Calculates the probability density function for the beta distribution at x.

Formula

let B(α, β) = Γ(α)Γ(β)/Γ(α + β)

x^(α - 1) * (1 - x)^(β - 1) / B(α, β)

where α is shapeA, β is shapeB, and Γ is the gamma function

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

Calculates the log probability density function for the beta distribution at x.

Formula

let B(α, β) = Γ(α)Γ(β)/Γ(α + β)

ln(x^(α - 1) * (1 - x)^(β - 1) / B(α, β))

where α is shapeA, β is shapeB, and Γ is the gamma function

impl ContinuousCDF<f64, f64> for Beta

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

Calculates the cumulative distribution function for the beta distribution at x

Formula

I_x(α, β)

where α is shapeA, β is shapeB, and I_x is the regularized lower incomplete beta function

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

Calculates the survival function for the beta distribution at x

Formula

I_(1-x)(β, α)

where α is shapeA, β is shapeB, and I_x is the regularized lower incomplete beta function

fn inverse_cdf(&self, p: T) -> K

Due to issues with rounding and floating-point accuracy the default implementation may be ill-behaved. Specialized inverse cdfs should be used whenever possible. Performs a binary search on the domain of cdf to obtain an approximation of F^-1(p) := inf { x | F(x) >= p }. Needless to say, performance may may be lacking.

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<R: Rng + ?Sized>(&self, rng: &mut R) -> f64

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl Distribution<f64> for Beta

fn mean(&self) -> Option<f64>

Returns the mean of the beta distribution

Formula

α / (α + β)

where α is shapeA and β is shapeB

fn variance(&self) -> Option<f64>

Returns the variance of the beta distribution

Remarks

Formula

(α * β) / ((α + β)^2 * (α + β + 1))

where α is shapeA and β is shapeB

fn entropy(&self) -> Option<f64>

Returns the entropy of the beta distribution

Formula

ln(B(α, β)) - (α - 1)ψ(α) - (β - 1)ψ(β) + (α + β - 2)ψ(α + β)

where α is shapeA, β is shapeB and ψ is the digamma function

fn skewness(&self) -> Option<f64>

Returns the skewness of the Beta distribution

Formula

2(β - α) * sqrt(α + β + 1) / ((α + β + 2) * sqrt(αβ))

where α is shapeA and β is shapeB

fn std_dev(&self) -> Option<T>

Returns the standard deviation, if it exists.

impl Max<f64> for Beta

fn max(&self) -> f64

Returns the maximum value in the domain of the beta distribution representable by a double precision float

Formula

1

impl Min<f64> for Beta

fn min(&self) -> f64

Returns the minimum value in the domain of the beta distribution representable by a double precision float

Formula

0

impl Mode<Option<f64>> for Beta

fn mode(&self) -> Option<f64>

Returns the mode of the Beta distribution.

Remarks

Since the mode is technically only calculate for α > 1, β > 1, those are the only values we allow. We may consider relaxing this constraint in the future.

Panics

If α <= 1 or β <= 1

Formula

(α - 1) / (α + β - 2)

where α is shapeA and β is shapeB

impl PartialEq for Beta

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

This method tests for self and other values to be equal, and is used by ==.

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

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

impl Copy for Beta

impl StructuralPartialEq for Beta