To define a lognormal distribution in Crystal Ball, you
need either a mean and a standard deviation, a log mean and a log standard
deviation, or a geometric mean and a geometric standard deviation.
However, if you have the most likely value (mode) and
any percentile, you can still define a lognormal distribution by converting
these values to one of these parameter sets.
Below is the derivation of the equations for the log
mean and log standard deviation from the mode and a percentile of a
lognormal distribution. You can download an example Excel workbook with
formulas already defined from:
http://www.decisioneering.com/download/lognorm.exe
Mode equation
The mode for a lognormal distribution is defined as:
(equation 3)
and
(equation 4)
Then, reduce equations 3 and 4, eliminating 
, to find:
(equation
5)
Solving this quadratic for the log standard deviation,
, finds:
(equation 6)
and substituting this for 
in equation 4 gives the log mean:
(equation 7)
Using new lognormal parameters in Crystal Ball
After you convert the mode and percentile value to
the log mean and the log standard deviation, you define your assumption
in Crystal Ball by:
- Select the cell to define.
- Select Cell > Define Assumption. The Distribution
Gallery appears.
- Select the Lognormal distribution.
- Click on OK. The Lognormal Distribution dialog
appears.
- From the Parms menu, select Log Mean, Log Stdev.
- Enter the calculated log mean and log standard
deviation in the fields.
- Click on OK.
(equation 1)
is the log mean and 
is the log standard deviation. 
) for a lognormal distribution is defined as:
(equation 2)
is the log mean, 
is the log standard deviation, and 
is a standard normal number (z score) for a given percentile. You
can find the standard normal number in a statistics book or you can
compute its value using the NORMSINV() function in Excel. 
and 