How to use the BETA.INV function
What is the BETA.INV function?
The BETA.INV function calculates the inverse of the cumulative beta distribution. This function has replaced the BETAINV function and was introduced in Excel 2010.
The beta distribution can help estimate how long a project might take by using the expected finish time and how variable the timeline could be. It gives the chance the project will be done at different dates based on the variability.
Table of Contents
1. Introduction
What is the inverse of the cumulative beta distribution?
The inverse of the cumulative beta distribution is a function that returns the value of x for a given probability p and parameters α and β of the beta distribution.
What is a cumulative beta probability distribution?
The cumulative beta distribution function gives the probability that a beta-distributed random variable with parameters α and β will be less than or equal to a given value x, providing the accumulated area under the probability density curve from 0 to x.
What is a beta probability density distribution?
A beta probability density distribution is a function whose shape over [0,1] depends on parameters α and β that gives the relative likelihood of a beta-distributed random variable occurring at different points, whose total area under the curve integrates to 1.
What are continuous values?
Continuous values are numbers that can take on any quantity within a range and can have infinitely many possibilities, unlike discrete values which have distinct separated values; continuous values can use intervals and ranges to describe events rather than fixed outcomes.
What are discrete probabilities?
Discrete probabilities are individual separated probabilities assigned to each of a countable number of possible outcomes that sum to 1, like rolling a die where each number has its own exact probability, as opposed to continuous distributions.
What are binomial success probabilities?
Binomial success probabilities describe the chance of a certain number of “successes” occurring in a fixed number of independent binary trial events modeled by the binomial distribution, like the probability of getting 3 heads in 10 coin flips.
What is Bayesian statistics?
Bayesian statistics is an approach to statistics using Bayes' theorem where prior beliefs about probabilities are updated as new evidence is acquired to determine conditional probabilities and update understanding of likelihood.
2. Syntax
The BETA.INV function has three required arguments and two optional arguments.
BETA.INV(probability,alpha,beta,[A],[B])
3. Arguments
| Argument | Description |
| probability | Required. |
| alpha | Required. A distribution parameter. |
| beta | Required. A distribution parameter. |
| [A] | Optional. Lower bound, default value 0 (zero). |
| [B] | Optional. Upper bound, default value 1. |
4. Example 1
The BETA.INV function calculates the inverse of the cumulative beta distribution representing an outcome between 0 and 1.
The BETA.DIST function is related to the BETA.INV function: BETA.INV(probability,alpha,beta,[A],[B]) = x
BETA.DIST(x,alpha,beta,cumulative,[A],[B]) = probability
A company manufactures a new product. The first 10 products has 7 working and 3 faulty. Assuming that the proportion of working products follows a beta distribution with parameters α = 8 and β = 4, find the values of the proportions corresponding to the 2.5th and 97.5th percentiles?
Alpha is the number of working products plus one and beta is the number of faulty products plus one. The ratio between the number of working products and the total number of products is 7/10 equals 0.7 The blue line has it's highest point at 0.7 if you check the x-axis.
The image above has argument
- probability in cell C18 and that value is 0.975
- alpha in cell C19
- beta in cell C20
Formula in cell C10:
The formula returns approx. 0.891 for a probability of 97.5% and approx. 0.390 for a probability of 2.5%.
There is a 97.5% probability that the proportion of working products is less than or equal to 0.891 (or 89.1%), assuming the given beta distribution parameters.
If the proportion of working products follows a beta distribution with parameters α = 8 and β = 4 the value of x so that the probability of observing a proportion less than or equal to x is 2.5% is approximately 0.390 or 39.0%.
5. Example 2
This example continues on example 1 above. The company has now manufactured 100 products, 90 working and 10 defect.
Assuming that the proportion of working products follows a beta distribution with parameters α = 91 and β = 11, find the values of the proportion corresponding to the 2.5th and 97.5th percentiles?
Alpha is the number of working products plus one and beta is the number of faulty products plus one. The ratio between the number of working products and the total number of products is 90/100 equals 0.9 The blue line has it's highest point at 0.9 if you check the x-axis.
The BETA.INV function returns 0.944 for 97.5% and 0.825 for 2.5 %.
This example shows that as the number of observations increases the probability density curve (blue) gets more narrow meaning the uncertainty is also decreasing. In other words, the function gets better as the number of observations increases.
6. Example 3
The optional arguments [A] and [B] are lower and upper limits respectively. The BETAINV function uses these limits to assist you calculating the x value for you which is a number between the lower limit and the upper limit.
You will get the same result if you calculate the x value yourself, here is an example.
The arguments are:
- probability = 0.921957262116145
- alpha = 90
- beta = 110
- [A] = 15
- [B] = 45
Formula in cell C7:
The formula in cell C7 returns 30.You can calculate x using only three arguments probability, alpha, and beta. Multiply the result with the total of the upper and lower limit to calculate x. It will be somewhere between the limits. Here is how:
returns 0.5
0.5*(15+45)=30 which is exactly what the function returns in cell C24
7. Function not working
The BETA.INV function returns
- #VALUE! error value if any argument is non-numeric.
- #NUM! error value if:
- alpha <= 0 (zero)
- beta <= 0 (zero)
- probability <= 0 (zero)
- probability > 1
- A = B
7.1 Troubleshooting the error value
When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.
- The first line describes the error if you press with left mouse button on it.
- The second line opens a pane that explains the error in greater detail.
- The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
- This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
- The fifth line lets you edit the formula in the Formula bar.
- The sixth line opens the Excel settings so you can adjust the Error Checking Options.
Here are a few of the most common Excel errors you may encounter.
#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.
#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.
#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.
#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.
#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.
#NAME error - The #NAME error happens if you misspelled a function or a named range.
#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.
#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.
#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.
7.2 The formula returns an unexpected value
To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that is really handy in these situations. Here is how to troubleshoot a formula:
- Select the cell containing the formula you want to examine in detail.
- Go to tab “Formulas” on the ribbon.
- Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control. - Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
- Repeat pressing the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
- Press "Close" button to dismiss the dialog box.
There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a feeling that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue.
- Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
- Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
- Press F9: This will calculate and display the result of just that selected portion.
- Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
- Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.
The image above shows cell reference C18 converted to hard-coded value using the F9 key. The BETA.INV function requires numerical values as input values which is not the case in this example. We have found what is wrong with the formula.
Tips!
- View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
- Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
- Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.
Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button
7.3 Other errors
Floating-point arithmetic may give inaccurate results in Excel - Article
Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.
Useful resources
Functions in 'Statistical' category
The BETA.INV function function is one of 73 functions in the 'Statistical' category.
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