Beta Distribution

The Beta distribution is a very versatile function which can be used to model several different shapes of probability density curves, as shown in the figure below.

$image\beta_dist.gif$

Beta (a1, a2) density functions. From Law (1991).

The form of the Beta distribution is determined by the shape parameters a1 and a2. Both a1 and a2 are always > 0. The relationship between the Beta distribution shape parameters and the RocSupport input data is as follows:

$image\beta_formula_1.gif$	Eqn. 1.
$image\beta_formula_2.gif$	Eqn. 2.

The standard deviation is the positive square root of the variance.

Note that Equations 1 and 2 apply to a beta random variable in the range [0, 1]. To obtain a beta random variable on [a, b] of the same shape, use the transformation a + (b–a) * X formula to rescale and relocate.