The Excel BETA.INV Function

BETA.DIST and BETA.INV

The Beta.Inv function is the inverse of the cumulative Beta.Dist function.

I.e. for a supplied probability, the Beta.Inv function returns the value of x such that:

probability = Beta.Dist( x, alpha, beta, True, [A], [B] )

Basic Description

The Excel BETA.INV function calculates the inverse of the cumulative beta probability density function for a supplied probability.

The Beta.Inv function is new to Excel 2010 and so is not available in earlier versions of Excel. However, the function is simply an updated version of the Betainv function, which is available in earlier versions of Excel.

The syntax of the Beta.Inv function is:

BETA.INV( probability, alpha, beta, [A], [B] )

Where the function arguments are:

probability-The probability of the Beta distribution, for which you want to find the value of x.
alpha-A parameter of the distribution (must be > 0).
beta-A parameter of the distribution (must be > 0).
[A]-

An optional numerical argument which gives the lower bound of the interval of x.

(If omitted, [A] takes the default value 0).
[B]-

An optional numerical argument which gives the upper bound of the interval of x.

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

Note that, if the arguments [A] and [B] are set to 0 and 1 respectively, this defines the Inverse Standard Cumulative Beta Distribution.


Beta.Inv Function Example

The charts on the left, below, shows the Cumulative Beta Distribution with the parameters alpha and beta set to 4 and 5, respectively. The interval of x is set to [0, 1], which makes this the Standard Cumulative Beta Distribution.

The chart on the right shows the Inverse of the Cumulative Beta Distribution, as calculated by the Beta.Inv function.

Plot of Standard Cumulative Beta Distribution with Alpha=4 and Beta=5
Standard Cumulative Beta Distribution Function with α = 4 and β = 5
Plot of Inverse Standard Cumulative Beta Distribution with Alpha=4 and Beta=5
Inverse Standard Cumulative Beta Distribution with α = 4 and β = 5

If you want to calculate the value of the Inverse Cumulative Beta Distribution for any probability (for example, the probability 0.2), this can be done by the Excel Beta.Inv function, as follows:

=BETA.INV( 0.2, 4, 5, 0, 1 )

This gives the result 0.303225845.

Note that, in the above example, the arguments [A] and [B] have been supplied as 0 and 1 respectively. However, these values could have been omitted from the function, as their default values are 0 and 1.


Further details and examples of the Excel Beta.Inv function are provided on the Microsoft Office website.


Beta.Inv Function Errors

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

Common Errors
#NUM!-

Occurs if either:

  • The supplied probability is ≤ 0 or ≥ 1;
  • The supplied values of [A] and [B] are equal;
  • The supplied alpha or beta is ≤ 0.
#VALUE!-Occurs if any of the supplied arguments are non-numeric.