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, 3 rd 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.