How to use the BETA.DIST function in Excel

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

What is 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. For example, there are two outcomes of an event, either success expressed as x, or failure expressed 1-x. Probability x can take value in interval [0, 1]. Now, suppose that we perform n independent repetitions of the experiment and we observe k successes and n-k failures. After performing the experiments, we need to know how we should revise the distribution initially assigned to x. In other words, we want to calculate the conditional distribution of x, conditional on the number of successes and failures we have observed. The result of this calculation is a Beta distribution. In particular, the conditional distribution of x, conditional on having observed k successes out of n trials, is a Beta distribution with parameters k+1 and n-k+1. The mathematical formulation for the beta distribution is complex and generally it depends on two parameters alpha and beta. How beta distribution behaves with changing alpha and beta values for the cumulative distribution and probability function shown below.

BETA.DIST Function in Excel

The Excel Beta.Dist function calculates 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.DIST Function syntax:

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

alpha : first parameter of the distribution

beta : second parameter of the distribution

cumulative : TRUE (returns cdf) or FALSE (returns pdf)

[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 beta distribution for the variable x ( =2 ) comes out to be 0.17. Now for the same parameters, find the beta probability distribution using the cumulative argument as FALSE as shown below.

Use the formula:

As you can see, the beta distribution for the variable x ( =2 ) comes out to be 0.77. 

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

1. The function only works with numbers. If any argument is nonnumeric, BETA.DIST 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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