Calculates the cumulative distribution function or the probability density function of a beta distribution.

### Syntax

BETADIST(x; α; β; a; b; cumulative)

The beta distribution is a family of continuous probability distributions, where α and β are parameters controlling the shape of the distribution.

x is the number, at which you will evaluate the Beta distribution.

The parameters a and b are lower and upper bounds of the distribution. You can interpret the value a as location and the value b−a as scale.

a and b are optional parameters which default (if omitted) to 0 and 1.

cumulative is an optional, logical parameter which defaults to TRUE() if omitted.

Before OOo version 3.1 the parameter cumulative doesn't exist and only the cumulative probability function is calculated.

Constraints:

1. α > 0 , β > 0 , a < b
2. If α < 1, than the density function has a pole at x = a.
3. If β < 1, than the density function has a pole at x = b.

### Semantic

For cumulative = FALSE() the function BETADIST calculates the probability density function (besides the constraints given above):



For cumulative = TRUE() the function BETADIST calculates the cumulative distribution function:



Notice, that



where



and  is the regularized incomplete Beta function.