How to use the LOGNORM.DIST function in Excel

In this article, we will learn How to use the LOGNORM.DIST function in Excel.

What is the 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 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,

Here

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.

Here

e is Euler's number ( value of e = 2.71828...).

x value at which 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

This formulation seems complex to formulate in Excel. So Excel provides a built-in statistical LOGNORM.DIST function to work as a lognormal distribution calculator.

LOGNORM.DIST Function in Excel

LOGNORM.DIST function built in statistical function returns the probability for the lognormal distribution. It takes the 3 arguments with the type of distribution function (cdf or pdf). Let's understand these arguments one by one listed below with the function syntax.

LOGNORM.DIST Function syntax:

=LOGNORM.DIST(x, mean, std_dev, cumulative)

x : value at which distribution is evaluated

mean : mean of lognormal distribution

std_dev : standard deviation of lognormal distribution

cumulative : logical value that determines the form of the function. If cumulative is TRUE, LOGNORM.DIST returns the cumulative distribution function; if FALSE, it returns the probability density function.

Example :

All of these might be confusing to understand. Let's understand how to use the function using an example. Here we have x value, mean and standard deviation. We need to calculate the cumulative for the lognormal distribution function.

Use the formula:

=LOGNORM.DIST ( B3, B4, B5, FALSE)

The lognormal distribution probability comes out 0.018 or 1.8% for the value exactly at 4 with mean 3.5 and standard deviation 1.2.

You can find out the probability value for the lognormal distribution function for the value at least 5 following the same parameters with the formula shown below.

Use the formula:

=LOGNORM.DIST ( B3, B4, B5, TRUE)

The lognormal distribution probability comes out 0.039 or 3.9% for the at least 4 value with mean 3.5 and standard deviation 1.2.

You can perform the inverse function of the lognormal distribution. Finding the x value using the probability value, mean value and standard deviation using the LOGNORM.INV function in Excel

Here are all the observational notes using the LOGNORM.DIST function in Excel
Notes :

The function only works with numbers. If any argument other than cumulative is non numeric, the function returns #VALUE! error.
The function returns #NUM! Error.
1. If argument x < 0
2. If argument mean <= 0
3. If argument std_dev < 0
Argument x event is truncated to integers if not.
The cumulative argument can be used with boolean numbers (0 and 1) or (FALSE or TRUE).
Value in decimal and value in percentage id the same value in Excel. Convert the value to percentage, if required.
You can feed the arguments to the function directly or using the cell reference as explained in the example.

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