BETA.DIST Function

Basic Description

The Excel BETA.DIST function calculates the cumulative beta distribution function or the beta probability density function, for a supplied set of parameters. The function was first introduced in Excel 2010 and so is not available in earlier versions of Excel. However, earlier versions of Excel do have the BETADIST function, which also calculates the cumulative beta distribution, but with slightly less accuracy.

Syntax: BETA.DIST( x, alpha, beta, cumulative, [A], [B] )

Where the function arguments are:

x The value at which the function is to be calculated (must be between [A] and [B])
alpha A parameter of the distribution (must be > 0)
beta A parameter of the distribution (must be > 0)
cumulative A logical argument that specifies the type of distribution to be used. This can be either:

TRUE = Cumulative Beta Distribution Function
FALSE = Beta Probability Density Function
[A] An optional argument which gives the lower bound of the interval of x

(if omitted, [A] takes the default value 0)

[B] An optional argument which gives the upper bound of the interval of x

(if omitted, [B] takes the default value 1)

If the arguments [A] and [B] are set to 0 and 1 respectively, this is the Standard Beta Distribution.

 

Beta.Dist Function Examples

Cumulative Beta Distribution Function Example

The chart on the right shows the Cumulative Beta Distribution with the parameter alpha set to 4 and the parameter beta set to 5.

The interval of x is set to [0, 1], which makes this the Standard Cumulative Beta Distribution.

If you want to use Excel to calculate the value of this function at x = 0.4, this can be done with the Beta.Dist function, as follows:

=BETA.DIST( 0.4, 4, 5, TRUE, 0, 1 )

This gives the result 0.4059136.

Plot of Standard Cumulative Beta Distribution with Alpha=4 and Beta=5

Standard Cumulative Beta Distribution Function with α = 4 and β = 5
Beta Probability Density Function Example

The chart on the right shows the Beta Probability Density Function with the parameters alpha and beta set to 4 and 5 respectively.

Again, the interval of x is set to [0, 1], which makes this the Standard Beta Probability Density Function.

If you want to use Excel to calculate the value of this function at x = 0.6, this can be done with the Beta.Dist function, as follows:

=BETA.DIST( 0.6, 4, 5, FALSE, 0, 1 )

This gives the result 1.548288.

Plot of Standard Beta Probability Function with Alpha=4 and Beta=5

Standard Beta Probability Density Function with α = 4 and β = 5

In both of the above examples, the arguments [A] and [B] have been supplied to both functions as the values 0 and 1. However, these values could have been omitted from the functions, as they would have then taken on the default values of 0 and 1.

 

Trouble Shooting

If you get an error from the Excel Beta.Dist function this is likely to be one of the following :

#NUM! Occurs if either the supplied x value is < [A] or > [B] or the supplied [A] and [B] arguments are equal or the supplied alpha or the supplied beta argument is ≤ 0
#VALUE! Occurs if any of the supplied arguments are non-numeric

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