Lognormal distribution



Jean Bréfort and Andreas J. Guelzowasked had an exchange about the lognormal distribution on 22 Aug.

There seems to be little documentation on how the randlognorm function works. We see in the help file:

Name
RANDLOGNORM
Synopsis
RANDLOGNORM(zeta,sigma)
Description
RANDLOGNORM returns a lognormal-distributed random number.
Examples
RANDLOGNORM(1,2).

It is correct as stated there that randlognorm returns a lognormally-distributed random number. But what the help documentation does not tell us is that the parameters zeta and sigma are for the normally distributed natural logarithm values. The function is evidently constructed in such a way that it returns random lognormal values using the mean and standard deviation (zeta and sigma respectively) of the normally distributed log values. So randlognorm(3.6586,0.2462) will return random lognormally distributed values having a mean of 40 and standard deviation of 10.

Thus if I am running a montecarlo simulation of a process that is assumed to have lognormally distributed process times with mean 40 and standard deviation 10, I must first calculate the mean (zeta) and standard deviation (sigma) of the normally distributed logarithms of the process times. The conversion between the normal and related lognormal parameters are clearly explained in most good statistics books, and at, for example the Wikipedia:

http://en.wikipedia.org/wiki/Log-normal_distribution

The NIST online "Engineering Statistics Handbook," for which a link was posted in the original post, is (to me) the most confusing description possible on this topic, and I do not recommend it, even though I am an engineer! The Dataplot software the NIST makes available is equally opaque. Not sure if this is of any help to others, and am brand new to the list, but it took me a while to figure it out and it may be worthwhile adding something to the Gnumeric help file.

Regards,

Carl






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