What Is GAMMA.INV function in Google Sheets?
The GAMMA.INV function in Google Sheets is used to calculate the inverse of the gamma cumulative distribution. It determines the value at which the cumulative distribution function (CDF) of the gamma distribution equals a given probability. The gamma distribution is used where the data is skewed, such as waiting times or life expectancy of equipment.
For example, suppose a student’s task completion time follows a gamma distribution with an alpha value of 1 and a beta value of 2. Let us discover the hours it would take to complete her tasks with an 80% probability. Enter the formula in a Google sheet:
=GAMMA.INV(0.7769, 1, 2).
You get a result of approximately 3 which indicates that there is a 80% chance the task will be completed within 3 hours.
Key Takeaways
- GAMMA.INV in Google Sheets returns the value x for which the cumulative gamma distribution equals a specified probability.
- The formula for GAMMA.INV is =GAMMA.INV(probability, alpha, beta). All the parameters must be positive.
- It is commonly used in forecasting, reliability analysis, and project planning to estimate the time or number thresholds based on known probabilities.
- Ensure the probability lies between 0 and 1; invalid inputs will result in a #NUM! error.
Syntax
The syntax of the GAMMA.INV function in Google Sheets is as follows:
=GAMMA.INV(probability, alpha, beta)
- probability: A number between 0 and 1 representing the cumulative probability for which you want to find the corresponding value in the gamma distribution.
- alpha: The shape parameter of the gamma distribution.
- beta: The scale parameter of the gamma distribution.
This function returns the value x such that GAMMA.DIST(x, alpha, beta, TRUE) = probability. This is the GAMMA INV Google sheets formula.
How To Use GAMMA.INV Function in Google Sheets?
We can use the GAMMA.INV function in Google Sheets to find the value corresponding to a given cumulative probability in a gamma distribution. It is very helpful when you know the probability and want to determine the threshold or cutoff value. You can enter the GAMMA.INV functions in the following ways:
- Enter the function manually
- Through the menu bar
Let’s explore how to use the function manually first.
Entering the Function Manually
Let us look at an example to understand this better. Suppose we have the delivery times for an online store. From the earlier data, we know that the delivery time for a product of the store follows a gamma distribution with an alpha value of 2 and a beta value of 4. We wish to calculate the maximum delivery time within which 85% of the deliveries are completed.\
Step 1: Let us first enter the values in a spread sheet.
B1 – 0.85 (probability)
- B2 – 2 (alpha)
- B3 – 4 (beta)
Step 2: Select the cell where you want the result. In cell D2, enter the following formula.
Type =GAMMA.INV(
Step 3: Enter the cell references or directly enter the values in the correct order. Here, we enter the references.
=GAMMA.INV(B1, B2, B3)
Close the parentheses.
Step 4: Press Enter. You will get a delivery time of roughly 13 hours within which 65% of packages are expected to arrive.
Using the Google Sheets Menu Bar
- Choose the cell where you want to display the result.
- Go to the top menu and click on “Insert” ➝ “Function” ➝ “Statistical” ➝ “GAMMA.INV.”
- Once the formula appears in the cell, fill in the arguments (probability, alpha, beta), and press Enter.
Examples
The GAMMA.INV function is useful when you wish to estimate a specific point in time or a value at which a given proportion of outcomes is expected to occur, based on a gamma distribution. Here are a few real-life cases to illustrate its use.
Example #1 – Estimate Insurance Claim Settlement Time
Let us look at an example where we estimate the time it typically takes to settle an insurance claim. Here, we assume that the settlement time follows a gamma distribution. The claim processing involves 4 steps, and each step takes an average of 3 days. We want to determine the maximum number of days within which 90% of claims are resolved.
Step 1: Let us enter the data in a sheet. The probability is 0.9, alpha is 4 (steps), and beta = 3 (each step takes 3 days).
Step 2: Click on an empty cell and type the following formula:
=GAMMA.INV(B1, B2, B3)
Step 3: Press Enter. The result will be approximately 20.04.
This means that around 90% of the insurance claims are expected to be fully processed within about 20.04 days, based on the given distribution.
Example #2 – Predict Project Completion Time for Dependent Tasks
Here, we look at a project that consists of several sequential tasks. The project includes 5 key stages, each taking 3 days. Let us estimate the time by which 75% of similar projects are completed.
Step 1: Let us input all the data in a spreadsheet.
Step 2: Enter the formula in cell B4.
=GAMMA.INV(B1, B2, B3)
Step 3: Press Enter to see the result. The function returns approximately 18.8.
This result indicates that 75% of projects are expected to be completed in about 18 days or less, on average.
Example #3 – Estimate Customer Wait Time in a Call Center Queue
We take the example of a call center that tracks the time customers wait before their issue is resolved. The resolution process has 3 stages which are receive, research, and resolve, and takes an average of 5 minutes. Let us find the wait time within which 90% of customers get their issues resolved.
Step 1: Let us enter all the data in a sheet.
- Probability = 0.9
- Alpha = 3 (three steps to resolve an issue)
- Beta = 5 (5 minutes for each step)
Step 2: Type the following formula in cell B4.
=GAMMA.INV(B1, B2, B3)
Step 3: Press Enter. You’ll get a result of that is 26.6.
The result tells us that 90% of customers expect the resolution of their issues in around 26.6 minutes or less. It helps in managing the staffing and setting customer expectations.
Important Things to Note
- We use the GAMMA.INV function to find the threshold value for a given cumulative probability within a gamma distribution.
- It is particularly helpful in reverse engineering the distribution to find the particular point to determine “how long” or “how much” corresponds to a known probability.
- The probability should be between 0 and 1; values outside this range will return a #NUM! error.
- GAMMA.INV always expects the alpha and beta parameters to be positive; A zero or negative value will return a #NUM! error.
Frequently Asked Questions (FAQs)
When you do not just stop with calculations but visualize your data, it can provide new perspectives based on the results. Once we calculate the GAMMA.INV results, we must use charts or graphs to understand the data better. We can create a scatter plot that helps visualize how changes in probability, alpha, and beta can affect the inverse gamma values. Charts also help identify patterns and trends. What are some of the errors we encounter when using GAMMA.INV in Google Sheets? Let us look at some errors we encounter while using GAMMA.INV and how to troubleshoot them.
● #NUM! Error: We get this error when the probability, alpha, or beta values are incorrect. Double-check these values to ensure they’re in the appropriate ranges.
● #VALUE! Error: We get this error when there’s a non-numeric value in our formula. Always check that all your inputs are numbers.
● Unclear Results: If the results are off, check that the parameters are right and the distribution is a gamma distribution.
It helps estimate the time by which there is a resolution of a certain percentage of customer support issues.
The value can predict the duration within which a certain percentage of deliveries will reach customers.
One uses it in reliability engineering to find the expected lifetime by which a percentage of machines may fail.
One uses it to plan project deadlines by identifying the time needed to complete a series of dependent tasks at a particular confidence level.
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This article must help understand GAMMA.INV Function in Google Sheets with its formulas and examples. You can download the template here to use it instantly.
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