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.