How to use the GAMMA function in Excel

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

What is the GAMMA function?

The gamma distribution is a two-parameter family of continuous probability distributions. The gamma distribution is the maximum entropy probability distribution. For example if you went to the station and to travel you need to buy the ticket. Ticket counter has a queue with a couple of people. Now given some fixed parameters, can you find the probability that you wait more than 5 minutes in the queue? Gamma distribution is used to predict the wait time until the k-th event. Now let's see how the parameters affect the probability factor. Gamma distribution(CDF) can be carried out in two types one is cumulative distribution function, the mathematical representation is given below.

Now we proceed to the other part which is probability density function which is extracted when you differentiate the above equation with respect to time. We get the below equation.

The red font part indicated in the denominator is basically the gamma factor. The gamma distribution plot is shown below.

As you can see these are complex functions to extract probability using it in excel. So excel provides the inbuilt statistical function to get gamma function results. Let's understand how to use the GAMMA function with an example.

GAMMA Function in Excel

The GAMMA function returns the gamma value . It takes the value and the two parameters named alpha and beta. Let's understand these arguments as explained below.

GAMMA Function syntax:

x : value at which you want to evaluate.

Example :

All of these might be confusing to understand. Let's understand how to use the function using an example. The Gamma Distribution is frequently used to provide probabilities for sets of values that may have a skewed distribution, such as queuing analysis. For example Waiting in a queue having 2 persons. The service times alpha and beta are independent with a mean of 2 minutes on each person. (Thus the mean service rate is .5/minute). Can you find the probability of waiting more than 5 minutes in the queue?

Use the formula:

As you can see there are very less chances of waiting in a queue for more than 5 minutes which is approximate 10%. I can wait for that period.

Now use the formula to find the probability density distribution. 

Use the formula:

As you can see how the new gamma function works in Excel.

Here are all the observational notes using the GAMMA function in Excel
Notes :

1. The function only works with numbers. If any argument other than cumulative is non numeric, the function returns #VALUE! error.
2. The function returns #NUM! Error.
   1. If x < = 0
   2. If x > 171.7
3. You can feed the arguments to the function directly or using the cell reference as explained in the example.

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