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.

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.

### Example

returns Invalid argument because there is a pole
returns 0

returns approximately 0.227