Struct statrs::distribution::Beta

source · [−]
pub struct Beta { /* private fields */ }
Expand description

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

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());

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);

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

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

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

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

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

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. Read more

Formats the value using the given formatter. Read more

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

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

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

Returns the mean of the beta distribution

Formula
ⓘ
α / (α + β)

where α is shapeA and β is shapeB

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

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

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

Returns the standard deviation, if it exists. Read more

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

Formula
ⓘ
1

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

Formula
ⓘ
0

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

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

This method tests for !=.

Auto Trait Implementations

Blanket Implementations

Gets the TypeId of self. Read more

Immutably borrows from an owned value. Read more

Mutably borrows from an owned value. Read more

Returns the argument unchanged.

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

Should always be Self

Performance hack: Clone doesn’t get inlined for Copy types in debug mode, so make it inline anyway.

Tests if Self the same as the type T Read more

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

Checks if self is actually part of its subset T (and can be converted to it).

Use with care! Same as self.to_subset but without any property checks. Always succeeds.

The inclusion map: converts self to the equivalent element of its superset.

The resulting type after obtaining ownership.

Creates owned data from borrowed data, usually by cloning. Read more

🔬 This is a nightly-only experimental API. (toowned_clone_into)

Uses borrowed data to replace owned data, usually by cloning. Read more

The type returned in the event of a conversion error.

Performs the conversion.

The type returned in the event of a conversion error.

Performs the conversion.