Definition:Beta Distribution

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Definition

Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $\Img X = \closedint 0 1$.


$X$ is said to have a Beta distribution if it has probability density function:

$\map {f_X} X = \dfrac {x^{\alpha - 1} \paren {1 - x}^{\beta - 1} } {\map \Beta {\alpha, \beta} }$

for $\alpha, \beta > 0$, where $\Beta$ is the Beta function.


This is written:

$X \sim \BetaDist \alpha \beta$


Also see

  • Results about the Beta distribution can be found here.


Technical Note

The $\LaTeX$ code for \(\BetaDist {\alpha} {\beta}\) is \BetaDist {\alpha} {\beta} .

When the arguments are single characters, it is usual to omit the braces:

\BetaDist \alpha \beta


Sources