What Is BETAINV Function in Google Sheets?
The BETAINV function in Google Sheets is used to calculate the inverse of the cumulative beta probability distribution function. Basically, is used to find the x-value for a given value of probability, alpha, and beta.
Imagine we must find the 70th percentile (or 0.7 probability) of a beta distribution with α = 3 and β = 5. In this example, α is less than β. Hence, the distribution is skewed to the right. The BETAINV function returns an x-value (between 0 and 1) where 70% of the probability mass lies below it. We enter the following function to get the result.
=BETAINV(0.7, 3, 5). Note that both BETA.INV and BETAINV are the same function in Google Sheets and are used to calculate the cumulative beta probability density function. However, BETA.INV is the newer, preferred function but BETAINV is retained and performs the same function. In some places in this article, we would be using it interchangeably and they mean the same.
Key Takeaways
- The BETAINV function in Google Sheets calculates the inverse of the beta distribution. It is often used in statistical analysis, particularly in scenarios involving probabilities and distributions in fields such as finance and quality control.
- The syntax of BETAINV in Google Sheets is as follows:
- =BETAINV(probability, alpha, beta, [A], [B])
a. probability: The probability associated with the Beta distribution
b. alpha: The alpha parameter of the Beta distribution
c. beta: The beta parameter of the Beta distribution
d. [A]: (Optional) The lower bound of the distribution.
e. [B]: (Optional) The upper bound of the distribution.
- The function is used in portfolio management to determine percentiles the returns for those that follow a Beta distribution.
Syntax And Parameters
Now that we have learnt the basic way in which the function is used, let us look at its syntax. The syntax of BETAINV or BETA.INV is as follows:
=BETA.INV(probability, alpha, beta, [lower_bound], [upper_bound)]
Parameters:
probability: (Mandatory) – It is a value between zero and one inclusive and is the probability at which to evaluate the function.
- alpha (Mandatory) – the first shape parameter of the distribution.
- beta (Mandatory) – the second shape parameter of the distribution.
- lower_bound (optional) – it is the lower bound of the original beta distribution’s domain.
- upper-bound (optional) – It is the upper bound of the original beta distribution’s domain.
How To Use BETAINV Function in Google Sheets?
Now that we have a brief introduction and learnt the syntax of BETAINV, let us look at how to use it in Google Sheets. To use BETA.INV in Google Sheets, there are two ways.
- One is to enter BETAINV manually
- Other way is to enter it through the menu bar.
Enter BETAINV Manually.
Let us look at how to calculate the inverse of the cumulative beta distribution function using BETA.INV entered manually. In this simple example, we have invested in two stocks. Let us enter the values in Google sheets. We wish to calculate the expected return for a 96% confidence interval.
Step 1: Let us calculate the alpha values of each stock.
For Stock A, the alpha value is (12%/20%) + 1 = 1.6.
For Stock B, the alpha value is (10%/24%) + 1 = 1.4.
Step 2: Next, to calculate the expected return for a 96% confidence interval using BETA.INV, enter the following function manually in Google Sheets as follows.
=BETA.INV(0.04,1.6,0.8,0).
Step 3: Press Enter. In cell B11, enter the following formula for Stock B.
=BETA.INV(0.04,1.4,0.6,0). Press Enter. The expected returns for Stock A and Stock B are 15.478% and 15.1%, respectively.
This, we can see how to enter the BETAINV function manually with a very practical example.
Entering the BETAINV Through the Menu Bar.
- Go to the Insert tab in Google Sheets.
- Select the option Function and then Statistical.
- From the list of functions, select the BETAINV or BETA.INV function and enter the arguments.
- Close the parentheses and press Enter to get the result.
Examples
Let us look at some interesting examples to understand BETAINV in Google Sheets better.
Example #1
Let us consider an organization organizing a regular lucky dip. The organization sold 1000 tickets lately and there were 78 winners. The organization claims that 1 in 12 of its customers are winners. Let us also verify if it is accurate. What is the 95% confidence interval for these numbers?
Step 1: For 1000 tickets, we have 78 winners. Hence, the alpha and beta values are 1000-78 = 922 and 78, respectively. Enter all the details in a sheet.
Step 2: Let us find the lower and upper bound for 95% confidence interval is
The probability argument is:
(1-0.95)/2 = 0.025.
Enter the following function in cell B4 for the lower bound.
= BETA.INV(.025, 78, 922). Press Enter.
Step 3: The upper bound of the 95% confidence interval is as follows. The probability is calculated as 1-0.025 = 0.975.
Enter = BETA.INV(.975, 78, 922). Press Enter.
Since 8.3% (1/12) is not in the 95% confidence, as we have got results of 6.22% and 9.54%, we conclude that the organization’s claim is not accurate with 95% confidence .
Example #2 – Estimate the Defect Rate of Electronic Products at a Given Probability
Let us look at how to use BETAINV in Google Sheets for quality assurance. A company is monitoring defect rates in its production process of electronic goods. We have to estimate the defect rate of the electronic products for a given probability.
Step 1: Let us choose the probability at which we wish to estimate the defect rate. Here, we use 97% probability as the upper bound.
Let us choose the Alpha and Beta parameters. We are expecting a 75% probability of defects and set alpha smaller than beta.
Hence, alpha = 3 and beta = 7.
Step 2: Enter the BETA.INV formula with the chosen parameters. For a probability of 75% and assuming alpha = 3 and beta = 7:
=BETA.INV(B1,B2,B3)
Step 3: The result provides an estimate of the defect rate at that probability.
Example #3 – Estimate a 75% Confidence Level for Positive Feedback From Customers
A business surveyed 500 customers and 380 provided positive feedback. Let the confidence interval be 75%.
Step 1: Enter the details in a Google Sheet.
The 75% confidence level corresponds to a probability of 0.75.
The alpha and beta parameters are assumed based on observed successes and failures.
Here, we have greater positive reviews and hence, Alpha is greater than beta.
Hence, alpha = 6 and beta = 4.
Step 2: For the lower bound, the probability is
(1-0.75)/2 = 0.125. Enter the following function in cell B4.
=BETA.INV(0.125,B2,B3).
Step 3: For the upper bound, use the formula in cell B5.
=BETA.INV(0.875,B2,B3).
Hence, the 75% confidence interval for the proportion of positive feedback is from 42.13% to 77.33%.
Important Things to Note
- The BETAINV function is the inverse function of BETA.DIST.
- The probability argument (first argument) should always be between 0 and 1.
- BETAINV usually returns a value that is between the A and B parameter range if they have been specified. Else, it returns a value between zero and one
- BETAINV finds the percentile for returns that follow a beta distribution when working with portfolio management or risk analysis.
Frequently Asked Questions (FAQs)
While the function is straightforward to use once the parameters are known,
1. BETAINV in Google Sheets returns the #VALUE! error value if any arguments are non-numeric.
2. If alpha or beta are ≤ zero, it returns the #NUM! error value.
3. If the probability argument is ≤ 0 or probability > 1, BETAINV returns the #NUM! error value.
4. For the optional arguments, if A is greater than B, we get an error.
The BETAINV in Google Sheets calculates the inverse of the cumulative beta probability distribution function, finding the value for a given probability within a beta distribution defined by its shape parameters, alpha and beta.
1) α = β: The distribution is symmetric.
2) α < β: The distribution is skewed to the right.
3) α > β: The distribution is skewed to the left.
4) α and β increase: The distribution becomes more concentrated around the mean.
Some of the functions similar to BETA.INV are:
BINOM.INV: It is used to calculate the inverse of the binomial cumulative distribution given a cumulative probability. The syntax is as follows:
=BINOM.INV(trials, probability_s, alpha)
It returns the number of successes in a binomial distribution with a fixed number of trials and a fixed probability of success.
NORM.INV: It returns the inverse of the normal distribution given a cumulative probability, it returns the corresponding value from a normal distribution with a specified mean and standard deviation. Its syntax is: =NORM.INV(probability, mean, standard_deviation).
Download Template
This article must help understand BETAINV Function in Google Sheets with its formulas and examples. You can download the template here to use it instantly.
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