How to use the BETA.INV function in Excel

In this article, we will learn How to use the  function in Excel.

What is Beta distribution and inverse beta distribution?

Beta Distribution is a continuous probability distribution function having a couple of parameters also known as alpha and beta. Generally, beta distribution is used to model one's uncertainty about the probability of success of an experiment. Whereas Inverted Beta cumulative distribution is also known as beta prime distribution. The beta prime distribution is the distribution of the odds ratio associated with a random variable with the beta distribution. Since variables with beta distributions are often used to model random probabilities and proportions, the corresponding odds ratios occur naturally as well. How beta distribution behaves with changing alpha and beta values for the inverted beta or Beta prime cumulative distribution shown below.

BETA.INV Function in Excel

The Excel BETA.INV function calculates the inverse of the cumulative beta distribution function or the probability density function of the Beta distribution, for a supplied set of parameters. Let's learn these parameters below.

BETA.INV Function syntax:

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

x : value between A and B at which to evaluate the function

alpha : first parameter of the distribution

beta : second parameter of the distribution

[A] : [Optional] lower bound to the interval of x. Default is 0

[B] : [Optional] upper bound to the interval of x. Default is 1


Example :

All of these might be confusing to understand. Let's understand how to use the function using an example. Here we have the parameters for a distribution and we need to find the beta cumulative distribution function

Use the formula:


As you can see, the inverse of beta distribution for the variable x ( = 0.2 ) comes out to be 0.06 whereas the normal beta distribution function returns the 0.30 for the same parameters.

Here are all the observational notes using the BETA.INV function in Excel
Notes :

  1. The function only works with numbers. If any argument is nonnumeric, BETA.INV returns the #VALUE! error value.
  2. Arguments to function can be fed directly or using the cell reference.
  3. If optional argument [A] and [B] are omitted. Default values are taken as 0 and 1. So x must lie between 0 and 1.
  4. The function returns #NUM error value :
    1. If alpha <= 0 or beta <= 0
    2. If x < A, x > B, or A = B

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