Lognormal Distribution

The lognormal distribution is a positive, right-skewed distribution: most values are moderate, but a few run much larger, which makes it a natural fit for task times that occasionally take a long while. A value is lognormal when its logarithm follows a normal distribution.

Write Lognormal(mu, sigma), where mu and sigma are the mean and standard deviation of the underlying normal, not of the values themselves:

Lognormal(2, 0.5)

Use it for service and handling times that cannot go negative and have a long right tail, where a symmetric normal would fit poorly. When you have real data, the Expression Builder can fit a lognormal to it and fill in the parameters for you, so there is nothing to work out by hand.

LegacyHow this worked in the previous version

When I generate a lognormal distribution in Stat::Fit it has 3 parameters. But when I copy and paste it to ProcessModel it only has 2. What do the parameters mean?

Answer

For the Lognormal distribution, Stat::Fit uses the parameters [min, mu, sigma] where min is the offset from 0, and mu, sigma are the mean and standard deviation of the included normal distribution. ProcessModel uses mean, sd which are the mean and standard deviation of the data after the offset is subtracted. The conversion is:

mean = exp(mu + (sigma^2)/2)
sd = exp(2*mu + sigma^2)*(exp(sigma^2) - 1)

You can find this and more in “Simulation Modeling & Analysis”, Law & Kelton, 3rd ed., 2000, p307.

Please note that Stat::Fit will do the conversion. Just open the Distribution Viewer for Lognormal, enter one set of parameters and the other set will be there as well. Also, the Distribution Viewer can be used to export to ProcessModel.