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.
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



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

beta1.png



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

beta2.png



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

beta3.png



BETADIST(1,5,3,-2,4,TRUE())
returns approximately 0.227


beta4.png



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

beta5.png



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

beta6.png









 
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