beta

final class boring_math.probability_distributions.distributions.beta.Beta

Bases: ContDist

Class for visualizing Beta distributions.

Note

The Beta distribution is a continuous probability distribution defined on (0, 1) with probability density function

f(x) = xᵅ⁻¹(1-x)ᵝ⁻¹/B(α,β) for α,β > 0

where

μ = α/(α+β)

σ² =  αβ/((α+β)²(α+β+1))

mode = (α-1)/(α+β-2) for α, β > 1

and B(α,β) = Γ(α)Γ(β)/Γ(α+β) is the normalization factor.

__init__(α: float, β: float)

__repr__() → str

Return repr(self).

pdf(x: float) → float

Beta probability distribution function.

cdf(x: float) → float

Beta cumulative probability distribution function.

__add__(other: Self) → Self

Fail if two Beta distributions are added.

Beta distributions are not stable, thus the sum of two random beta distributed variables is not Beta distributed.