# BETA.INV

The `BETA.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.

## Usage

Use the `BETA.INV` formula with the syntax shown below, it has 3 required parameters and 2 optional parameters:

Parameters:
1. probability (required):
The probability for which you want to find the inverse cumulative distribution function.
2. alpha (required):
The alpha parameter of the beta distribution.
3. beta (required):
The beta parameter of the beta distribution.
4. lower_bound (optional):
The lower bound of the distribution, defaults to 0 if not specified.
5. 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 the `BETA.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). Double-check the value you entered.

### Invalid alpha or beta value

The alpha and beta arguments must be greater than 0. Double-check 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. Double-check the values you entered.

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 t-distribution for the provided probability and degrees of freedom. This function is commonly used to calculate a critical value from the t-distribution 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.

You can learn more about the `BETA.INV` Google Sheets function on Google Support.