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anylogic
Diederik Huijsman
Diederik Huijsman

Reputation: 43

How do I calculate log-normal distributed mean from 'mean of included normal'?

The question I have seems a bit unclear. Let me explain what I mean:

I'm trying to recreate a distribution from a paper in anylogic, which gives the mu and sigma^2 for a log-normal distribution EXPLICITLY: when I model the mu = 12 and sigma^2=36 from the paper in the built-in AnyLogic function: lognormal(double mu, double sigma, double min) as lognormal(12.0, 6.0, 0.0) because it cannot be negative. The function however gives values in the several ten-thousands or even millions. I was expecting WAY lower values. I know this for sure, because the value dictates customer required lead-times, and the model only runs for about 6000 hours.

I realized the text on the log-normal distributions AnyLogic help website: "sigma = The standard deviation of the included Normal."

What does that mean for the given distributions from the paper? Am I missing calculations between Normal and log-Normal distributions?

Upvotes: 0

Views: 759

Answers (1)

Felipe
Felipe

Reputation: 9421

the distributions are generally very well documented if you do a google search. From wikipedia:

In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.

so the following statement

sigma = The standard deviation of the included Normal

Means exactly what it says... there's a random variable who follows a normal distribution, and this is the sigma they are talking about here... the sigma of the normally distributed variable.

To calculate the mean of a lognormal you do the following:

Mean = exp (mu + 0.5*sigma^2)

in your case, it would be exp(30)=1.068647e+13 So a pretty big number

many people think that normal and log-normal are the same for some reason, so either the paper is wrong or you are wrong, i don't have access to the paper to know

Upvotes: 1

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