Beta Distribution

Probability · Axiom Academy

A flexible distribution on [0,1] for modeling proportions and probabilities 1. Probability Density Function The Beta PDF is defined on [0, 1] with shape parameters α and β. The Beta function B(α, β) in the denominator ensures the PDF integrates to 1. Different parameter values create vastly different shapes. When α = β = 1, we get the uniform distribution. When α = β > 1, the distribution is symmetric and bell-shaped. When α ≠ β, the distribution is skewed. When both are less than 1, the distribution is U-shaped. The Beta distribution is the conjugate prior for the Bernoulli and binomial distributions in Bayesian inference. It's also used to model random variables that are naturally bounded between 0 and 1, such as proportions, probabilities, and percentages.

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