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

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:

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

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.

BETADIST(1,5,3,-2,4,FALSE())returns approximately 0.273

BETADIST(0.2,0.7,4,0,1,FALSE())returns approximately 1.644

BETADIST(1,1,0.5,0,1,FALSE())

returns Invalid argument because there is a pole

BETADIST(1.1,1,0.5,0,1,FALSE())

returns 0

BETADIST(1,5,3,-2,4,TRUE())

returns approximately 0.227

BETADIST(0.2,0.7,4,0,1,TRUE())returns approximately 0.718

BETADIST(1.1,1,0.5,0,1,TRUE())returns 1

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