Beta distribution (probability density function)

Description

In probability theory and statistics, the beta distribution is a family of continuous probability distributions parametrized by two positive shape parameters, denoted by α and β, that appear as exponents of the random variable and control the shape of the distribution.The usual formulation of the beta distribution is also known as the beta distribution of the first kind. A probability density function (pdf), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.

Related formulas

Variables

pdfProbability density function (dimensionless)
xRealization -observed value that actually occurred—of a random process X (dimensionless)
αShape parameter (α>0) (dimensionless)
βShape parameter (β>0) (dimensionless)
BBeta function (dimensionless)