BETA.INV
TheBETA.INV
function returns the inverse of the cumulative distribution function for a specified beta distribution with parameters alpha and beta. This function is commonly used in statistical analysis to find the value at which a specified probability occurs within a beta distribution. The function takes in the probability and the values for alpha, beta, lower bound, and upper bound to calculate the inverse function.
 How to use
BETA.INV
formula?  Examples of using
BETA.INV
formula BETA.INV
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BETA.INV
Usage
Use the BETA.INV
formula with the syntax shown below, it has 3 required parameters and 2 optional parameters:
 probability (required):
The probability for which you want to find the inverse cumulative distribution function.  alpha (required):
The alpha parameter of the beta distribution.  beta (required):
The beta parameter of the beta distribution.  lower_bound (optional):
The lower bound of the distribution, defaults to 0 if not specified.  upper_bound (optional):
The upper bound of the distribution, defaults to 1 if not specified.
Examples
Here are a few example use cases that explain how to use theBETA.INV
formula in Google Sheets.
Finding the critical value for a beta distribution
Suppose you are given a beta distribution with alpha = 5 and beta = 10. You want to find the critical value at which 95% of the observations are below that value. You can use the BETA.INV
function to find that value by setting probability to 0.95, alpha to 5, and beta to 10.
Calculating the probability of an observation in a beta distribution
Suppose you have a beta distribution with alpha = 2 and beta = 4, and you want to find the probability of an observation being less than or equal to 0.3. You can use the BETA.INV
function with lower_bound set to 0, upper_bound set to 0.3, probability set to 1, and alpha set to 2 and beta set to 4 to find the value at which 100% of the observations are below 0.3. Subtract this value from 0 to get the probability of an observation being greater than 0.3.
Generating random numbers from a beta distribution
Suppose you want to generate random numbers from a beta distribution with alpha = 3 and beta = 2. You can use the BETA.INV
function with probability set to RAND()
, alpha set to 3, and beta set to 2 to generate a random number from the beta distribution.
Common Mistakes
BETA.INV
not working? Here are some common mistakes people make when using the BETA.INV
Google Sheets Formula:
Missing arguments
One or more arguments are missing. Make sure to include all required arguments in the formula.
Incorrect argument type
One or more arguments have an incorrect type. Check the syntax and make sure all arguments are of the correct type.
Invalid probability value
The probability argument must be between 0 and 1 (inclusive). Doublecheck the value you entered.
Invalid alpha or beta value
The alpha and beta arguments must be greater than 0. Doublecheck the values you entered.
Invalid bounds
The lower and upper bounds must be between 0 and 1 (inclusive) and the lower bound must be less than the upper bound. Doublecheck the values you entered.
Related Formulas
The following functions are similar to BETA.INV
or are often used with it in a formula:

BETA.DIST
The
BETA.DIST
function returns the beta cumulative distribution function, which describes the probability of a value falling between two bounds. This function is commonly used in statistical analysis to model data that is continuous and bounded between 0 and 1. The function takes in parameters for the value, alpha, beta, cumulative, lower bound, and upper bound. 
GAMMA.INV
The
GAMMA.INV
formula returns the inverse of the cumulative distribution function for a specified probability and the Gamma distribution. It is commonly used in statistical analysis to find the value at which a specified percentage of the distribution lies. The Gamma distribution is a continuous probability distribution that is used to model the time until a certain number of events occur. 
NORM.INV
The
NORM.INV
function returns the inverse of the cumulative normal distribution for a specified mean and standard deviation. It is commonly used in statistical analysis to find the value at which a specified percentage of observations occur below that value. 
T.INV
The
T.INV
function returns the inverse of the Student's tdistribution for the provided probability and degrees of freedom. This function is commonly used to calculate a critical value from the tdistribution when working with small sample sizes. 
BINOM.INV
The
BINOM.INV
formula calculates the smallest value for which the cumulative binomial distribution is less than or equal to a specified criterion value. It is commonly used in statistics to find the exact number of successes in a fixed number of independent trials with a known probability of success.
Learn More
You can learn more about the BETA.INV
Google Sheets function on Google Support.