Lognormal distribution parameters mu and sigma
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Hi,
I want to generate a lognormal distribution for a set of data measurments using Simbiology model analyzer. I need to insert the mu and sigma for of this distribution as shown in the attachment. Is mu=log(mean) and sigma=log(Standard deviation)?
Thank you!
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Accepted Answer
John D'Errico
on 9 Apr 2024
Edited: John D'Errico
on 9 Apr 2024
In MATLAB, the tools that use a lognormal distribution have you provide mu and sigma in terms of the underlying normal distribution. For example...
help lognrnd
In that help, you can see how to choose mu and sigma, IF you know the mean and variance of the distribution you wish to see.
That is, if you know the mean and variance of the lognormal distribution you wish, choose mu and sigma as:
MU = log(M^2 / sqrt(V+M^2))
SIGMA = sqrt(log(V/M^2 + 1))
For example, choosing a lognormal with mean 2, and standard deviation 0.5 (so a variance of 0.25) we would see:
M = 2;
V = 0.25;
MU = log(M^2 / sqrt(V+M^2))
SIGMA = sqrt(log(V/M^2 + 1))
X = lognrnd(MU,SIGMA,[1e8,1]);
mean(X)
std(X)
And that is exactly what we would expect from a random sample. I believe Simbiology would use the same version of a lognormal distribution.
More Answers (1)
Bruno Luong
on 9 Apr 2024
Edited: Bruno Luong
on 9 Apr 2024
Is mu=log(mean) and sigma=log(Standard deviation)?
If X is log-normal random variable
- mu is mean of log(X)
- sigma is standard deviation of log(X)
- log(X) is Gaussian random variable
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