# BETAINV

The `BETAINV` function returns the inverse of the cumulative distribution function for a specified beta distribution. This function is commonly used in statistical analysis to estimate the shape of probability distributions. The function takes in a probability value, the two shape parameters of the beta distribution, and lower and upper bounds of the distribution, and returns the value of the random variable that corresponds to the specified probability.

## Usage

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

Parameters:
1. probability (required):
The probability value for which to evaluate the inverse of the cumulative distribution function.
2. alpha (required):
The first shape parameter of the beta distribution.
3. beta (required):
The second shape parameter of the beta distribution.
4. lower_bound (optional):
An optional lower bound of the distribution, default is 0.
5. upper_bound (optional):
An optional upper bound of the distribution, default is 1.

## Examples

Here are a few example use cases that explain how to use the `BETAINV` formula in Google Sheets.

### Estimate the probability of success for a given number of trials

Suppose you conduct an experiment in which a coin is flipped 10 times and it lands heads up 6 times. You can use the `BETAINV` function to calculate the probability of getting 6 or fewer heads in 10 flips, given that the coin is fair. This can be useful in determining whether the coin is actually fair or not.

### Estimate the probability of a stock price increase

Suppose you are analyzing the daily returns of a stock and want to estimate the probability of the stock price increasing by at least 5% in the next month. You can use the `BETAINV` function to estimate the shape of the distribution and calculate the corresponding probability.

### Calculate the expected value of a beta distribution

The expected value of a beta distribution is given by the formula `alpha / (alpha + beta)`. You can use the `BETAINV` function to estimate the shape parameters of the distribution and then calculate the expected value.

## Common Mistakes

`BETAINV` not working? Here are some common mistakes people make when using the `BETAINV` Google Sheets Formula:

### Incorrect probability value

One of the most common mistakes when using the BETAINV formula is to provide a probability value that is not between 0 and 1. This can result in unexpected results or errors. To correct this mistake, ensure that the probability value is between 0 and 1.

### Switched alpha and beta values

Another common mistake is to switch the order of the alpha and beta values. This can result in incorrect calculations. To correct this mistake, ensure that the alpha value is provided before the beta value.

### Incorrect order of bounds

It is important to provide the lower bound value before the upper bound value in the BETAINV formula. Switching the order of these values can result in incorrect calculations. To correct this mistake, ensure that the lower bound value is provided before the upper bound value.

The following functions are similar to `BETAINV` or are often used with it in a formula:

• `BETADIST`

The `BETADIST` formula returns the cumulative beta distribution function. It is commonly used in statistical analysis to model events that result in outcomes between two bounds. The distribution is defined by the beta function, which is a continuous probability distribution with support from 0 to 1. The function can be used to determine the probability of a random variable falling between two values.

• `BINOM.DIST`

The `BINOM.DIST` function returns the probability of a certain number of successes in a fixed number of trials given a probability of success in each trial. It is most commonly used in statistical analysis and hypothesis testing. The function can calculate either the probability mass function (PMF) or the cumulative distribution function (CDF) depending on the value of the `cumulative` parameter.

• `NORMINV`

The `NORMINV` function returns the inverse of the normal cumulative distribution for a specified value, mean, and standard deviation. It is commonly used in statistics to find the value at which a given percentage of observations lie below that value.

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