In this article, we will learn How to use the LOGNORM.INV function in Excel.
What is the lognormal distribution function and inverse of lognormal distribution function ?
In Statistics, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. A random variable which is log-normally distributed takes only positive real values. It is a convenient and useful model for measurements in exact and engineering sciences as well as medicine, economics and other fields, e.g. for energies, concentrations, lengths, financial returns and other amounts. So if the data has x1,x2, x3, ...etc values, then the lognormal distribution has ln(x1), ln(x2), ln(x3), ...etc values. Now our new random variable becomes new x1, new x2,..
So inversely we can say x1 = e^(new x1) as shown below,
e is Euler's number ( value of e = 2.71828...).
Lognormal distribution is often applicable in time to repair equipment, time to fatigue failure or economic data, basically saying while getting the idea for maintenance things or values. Mathematically, we can calculate the probability for lognormal distribution function using the formula stated below.
e is Euler's number ( value of e = 2.71828...).
x value at which inverse of lognormal distribution is evaluated
x , mean , std is the value, mean and standard deviation for the normal distribution
x' , mean', std' is the value, mean and standard deviation for the lognormal distribution.
We calculate the probability value for x value using the LOGNORM.DIST function. But if you want to find out the value x from the lognormal probability value using the mean and standard deviation.
This formulation seems complex to formulate in Excel. So Excel provides a built-in statistical LOGNORM.INV function to work as an inverse of lognormal distribution calculator.
LOGNORM.INV Function in Excel
LOGNORM.INV function built in statistical function returns the x value for the probability of lognormal distribution. It takes the 3 arguments. Let's understand these arguments one by one listed below with the function syntax.
LOGNORM.INV Function syntax:
|=LOGNORM.INV(probability, mean, std_dev)|
probability : probability value for the distribution
mean : mean of inverse for lognormal distribution
std_dev : standard deviation for inverse of lognormal distribution
All of these might be confusing to understand. Let's understand how to use the function using an example. Here we have probability value, mean value and standard deviation value. We need to calculate the x value for the inverse of lognormal distribution function.
Use the formula:
|=LOGNORM.INV ( B3, B4, B5 )|
The x value for the lognormal distribution comes out 4for the value probability value 0.039 or 3.9% with mean 3.5 and standard deviation 1.2.
You can perform the inverse of this function i.e. you can find the probability value using the x value, mean value and standard deviation value for the lognormal distribution using the LOGNORM.DIST function. Use the cumulative argument as TRUE to get the x value value.
Here are all the observational notes using the LOGNORM.INV function in Excel
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