Documentation/How Tos/Calc: BETADIST function

BETADIST

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.

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 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.

Example

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 illegal argument because there is a pole

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

returns 0

See also

BETAINV

Statistical functions

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