2.1.1.13. Beta law
Defined between a minimum and a maximum, it depends on two parameters \(\alpha\) and \(\beta\), as
\[f(x) = \frac{Y^{\alpha - 1}\times ( 1 - Y )^{\beta - 1}}{B(\alpha,\beta)} \;
{\rm 1\kern-0.28emI}_{[x_{\rm min},x_{\rm max}]}(x)\]
where \(Y =\dfrac{(x-x_{\rm min})}{(x_{\rm max}-x_{\rm min})}\) and \(B(\alpha,\beta)\) is the beta function.
Figure 2.14 shows the PDF, CDF and inverse CDF generated for different sets of parameters.
Figure 2.14 Example of PDF, CDF and inverse CDF for Beta distributions.
