# LOGNORM.INV

The `LOGNORM.INV` function returns the inverse of the lognormal cumulative distribution for a specified mean and standard deviation. It is commonly used in statistics to model data that is skewed and has a long tail. Given a percentile value and the distribution parameters, this function calculates the corresponding value of the random variable.

## Usage

Use the `LOGNORM.INV` formula with the syntax shown below, it has 3 required parameters:

Parameters:
1. x (required):
The probability associated with the lognormal distribution. Must be a value between 0 and 1.
2. mean (required):
The mean of the lognormal distribution. Must be greater than 0.
3. standard_deviation (required):
The standard deviation of the lognormal distribution. Must be greater than 0.

## Examples

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

### Calculating investment returns

Suppose you have an investment portfolio with a mean return of 8% and a standard deviation of 3%. You want to know the return that corresponds to the 95th percentile of the distribution. You can use `LOGNORM.INV` to calculate this value.

### Modeling stock prices

Stock prices often follow a lognormal distribution. You can use `LOGNORM.INV` to model the price of a stock at a future date based on its current price, mean return, and standard deviation of returns.

### Estimating failure rates

In reliability engineering, the lognormal distribution is often used to model the time to failure of a system. `LOGNORM.INV` can be used to estimate the failure rate corresponding to a given percentile of the distribution.

## Common Mistakes

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

### Incorrect argument order

Users may accidentally input the mean as the second argument and the standard deviation as the third argument, causing the formula to return incorrect results. The correct order is to input the value of x first, followed by the mean and standard deviation.

### Invalid input data type

Users should ensure that the input values for x, mean, and standard deviation are numeric. Non-numeric values will cause the formula to return an error.

### Incorrect mean or standard deviation value

Users should ensure that the mean and standard deviation values are positive. Negative values will cause the formula to return an error.

### Incorrectly interpreting the output

The output of LOGNORM.INV is the inverse of the cumulative distribution function of the log-normal distribution. Users should ensure that they interpret the output correctly based on their specific use case and context.

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

• `LOGNORM.DIST`

The `LOGNORM.DIST` function returns the cumulative distribution function (CDF) of the log-normal distribution, given a value x, a mean and a standard deviation. The log-normal distribution is often used to model values that are inherently positive and have a large range of values. The function is commonly used in financial analysis to model stock returns and in engineering to model the size of particles in a material.

• `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.

• `NORM.DIST`

The `NORM.DIST` formula is a statistical function that returns the normal distribution of a specified variable. It is used to determine the probability of a random variable falling within a specified range of values. This function is commonly used in finance and scientific research.

• `EXPON.DIST`

The EXPON.DIST function returns the exponential distribution of a specified random variable, x, given a specified lambda, LAMBDA. The exponential distribution is commonly used to model the time between events in a Poisson process. The function returns the probability density function or the cumulative distribution function of the exponential distribution depending on whether the cumulative argument is set to TRUE or FALSE. This function is useful for analyzing reliability data and can be used to determine the probability that a component will fail before a certain time.

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