GAMMA.DIST in Google Sheets

What Is GAMMA.DIST function in Google Sheets?

In Google Sheets, the GAMMA.DIST function calculates the probability density function (PDF) or cumulative distribution function (CDF) of the gamma distribution, a two-parameter continuous probability distribution. The GAMMA.DIST function is used in statistics to model the time until an event happens a particular number of times. Unlike the bell-shaped normal distribution, this function works when the time is skewed. Some examples of its use include queuing systems (for instance, the time taken for the first three customers to arrive) or predicting the time until a machine fails multiple times. We use it in scenarios such as when we wish to know the probability that a machine fails after 10 hours, given that it usually happens around 6 hours.

Let’s see how long it takes a student to complete her daily tasks. Based on past data, the process is best modeled by a gamma distribution with alpha =1 and beta = 2. Let us find the probability that the student completes her daily task in 3 hours.

=GAMMA.DIST(3, 1, 2, TRUE). TRUE means we need the cumulative probability.

The GAMMA distribution formula returns 0.7769, meaning there’s about a 77.69% chance the task is completed within 3 hours under this distribution.

Syntax

The syntax of the GAMMA.DIST function in Google Sheets is as follows:

=GAMMA.DIST(x, alpha, beta, cumulative)

1. x: The value for which we will evaluate the distribution.
2. alpha: The shape of the gamma distribution.
3. beta: The scale of the gamma distribution.
4. cumulative: TRUE or FALSE value to return the PDF (FALSE) or CDF (TRUE).

How To Use GAMMA.DIST Function in Google Sheets?

We can use GAMMA.DIST in Google Sheets to calculate the probability density function or cumulative distribution function of a gamma distribution for a given value of x. We can enter the GAMMA.DIST function as follows:

1. Manually enter the GAMMA.DIST function
2. Through the menu bar

Let us look at how to do it manually.

Step 1: The first step is the preparation of our data. To understand the function better, we use a simple example. We are tracking call durations received from customers at a store. We notice that the time until 5 calls are over, and it follows a gamma distribution. Each call takes 3 minutes on average. Here, we will find the probability that all five calls finish within 10 minutes.

Enter the details on a sheet as shown below.

 Step 2: To calculate the CDF of the distribution (as we are finding the probability up to 10 minutes and not AT 10 minutes), we use GAMMA.DIST. Enter the following formula manually.

Type =GAMMA.DIST( in cell D3.

Step 3: Either manually enter the parameters or enter their cell references. Here, we enter the cell references of the parameters in the following order, separated by commas. Close the parentheses.

=GAMMA.DIST(A2,B2, C2, D2)

Step 4: Press Enter, and we get the probability. Convert it to a percentage by clicking on the Percent icon in the top bar.

Using the Google Menu bar

1. Choose the cell where you want to enter the formula.
2. Go to the menu bar and click on “Insert” ➝ “Function” ➝ “Statistical” ➝ “GAMMA.DIST.”
3. Once the function is entered in Google Sheets, enter the required arguments and press Enter.

Examples

The gamma distribution helps model the total time until a particular number of events take place, given that each event takes a particular amount of time. Need more clarity? Here are some interesting examples to understand the same.

Example #1 – Probability Density Function

In this example, let us analyze the lifetime of a machine. It follows a gamma distribution. Let us find out the probability that the machine will fail in 10 days. Here, the failure happens after 3 events. So, alpha is 3. The time between failures is 5 days. So, beta = 5.

Here, we must find the GAMMA distribution PDF, that is, instead of finding the probability it will fail within 10 days, we must find the probability of failure on exactly the tenth day.

Step 1: Let us enter these details in a sheet.

Let

1. x = 10 (the time you’re evaluating)
2. alpha = 3 (3 events)
3. beta = 5 (average time per event)
4. cumulative = FALSE (to find the GAMMA distribution PDF)

Step 2: Let us enter the following formula to find the probability of failure on exactly the tenth day.

=GAMMA.DIST(A2,B2,C2,D2). Press Enter.

You’ll get around 0.05413.

This result means that the probability density at 10 days is 0.05413. So, there’s a 5% chance of the machine’s likely failure at around 10 days.

Example #2 – Cumulative distribution function

In this example, a person is solving some difficult Math problems and expects to solve one every 15 minutes. Let us find the probability that it would take up to 2 hours to solve six problems.

Step 1: Enter the parameters as shown below.

Parameters for GAMMA.DIST:

1. x = 2 – Time taken is up to two hours
2. alpha = 6 – We must finish six problems.
3. beta = 0.25 – Average time taken for one problem is 15 minutes
4. cumulative = TRUE → Because we want the probability up to 2 hours

Step 2: Enter the following formula in Google Sheets.

=GAMMA.DIST(2, 6, 0.25, TRUE). Press Enter.

Step 3: We get the result as approximately 0.808 or 80.8%. It means that there is an 80% chance that the person will complete all six problems within two hours at an average of 15 minutes per problem.

Example #3

Let us take a practical example of a gamma distribution where we will model the time it takes for a customer care center to receive a certain number of calls. Here, we know the details, where we will be finding the probability of receiving 7 calls in the next 15 minutes. Calls come at an average of 1 call every 3 minutes.

Step 1: Enter the parameters as shown below.

1. alpha = 7 as 7 calls
2. beta = 3 as each call takes an average of 3 minutes
3. x = 15 as we’re finding the time up to 15 minutes
4. cumulative = TRUE

Step 2: Enter the following formula in Google Sheets.

=GAMMA.DIST(A2,B2,C2,D2). Press Enter.

Step 3: We get the result as approximately 0.2378. It means that there is a 23.78% chance that we will receive 7 calls within 15 minutes at an average of 3 minutes per call.

Important Things to Note

1. One uses the GAMMA.DIST function in continuous probability distributions to model the waiting time between events, like the time between two customer calls or the time between two natural calamities.
2. GAMMA.DIST in Google Sheets is used in finance to model the rate of return on an investment.
3. It is also widely used to model the income distribution of a population in economics.

Frequently Asked Questions (FAQs)

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