The Excel LOGNORM.DIST Function

Related Functions:
NORM.DIST
LOGNORM.INV
Log-Normal Distribution

A variable x is Log-Normally Distributed if its natural logarithm is normally distributed.

In terms of Excel functions: where μ is the mean of ln(x) and σ is the standard deviation of ln(x).

Function Description

The Excel LOGNORM.DIST function calculates the Log-Normal Probability Density Function or the Cumulative Log-Normal Distribution Function for a supplied value of x.

The Lognorm.Dist function is new in Excel 2010 and so is not available in earlier versions of Excel. However, the function is just an updated version of the Lognormdist function, which is available in earlier versions of Excel.

The syntax of the Lognorm.Dist function is:

LOGNORM.DIST( x, mean, standard_dev, cumulative )

Where the function arguments are listed in the following table:

x-The value at which you want to evaluate the log-normal distribution function.
mean-The arithmetic mean of ln(x).
standard_dev-The standard deviation of ln(x).
cumulative-

A logical argument which denotes the type of distribution to be used:

 TRUE = Cumulative Normal Distribution Function FALSE = Normal Probability Density Function

Lognorm.Dist Function Examples

Example 1 - Normal Probability Density Function Log-Normal Probability Density Function with mean ln(x) = 10 & std. dev. ln(x) = 5

The above chart on the right shows the Log-Normal Probability Density Function for a variable, x. The mean of ln(x) is 10 and the Standard Deviation of ln(x) is 5.

If you want to calculate the value of this function at x = 0.5, this can be done using the Excel Lognorm.Dist function, as follows:

=LOGNORM.DIST( 0.5, 10, 5, FALSE )

This gives the result 0.016210482.

Example 2 - Cumulative Log-Normal Distribution Function Log-Normal Cumulative Distribution with mean ln(x) = 10 & std. dev. ln(x) = 5

The above chart on the right shows the Log-Normal Cumulative Distribution Function for a variable x. Again, the mean of ln(x) is 10 and the Standard Deviation of ln(x) is 5.

If you want to calculate the value of this function at x = 12, this can be done using the Excel Lognorm.Dist function, as follows:

=LOGNORM.DIST( 12, 10, 5, TRUE )

This gives the result 0.066417115.

For further information and examples of the Excel Lognorm.Dist function, see the Microsoft Office website.

Lognorm.Dist Function Errors

If you get an error from the Excel Lognorm.Dist function this is likely to be one of the following:

Common Errors
 #NUM! - Occurs if the supplied x ≤ 0 or the supplied standard_dev ≤ 0. #VALUE! - Occurs if any of the supplied arguments is non-numeric.