Lognormal distribution parameters mu and sigma

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Day 2024-4-9

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https://ww2.mathworks.cn/matlabcentral/answers/2104946-lognormal-distribution-parameters-mu-and-sigma

编辑： Jeremy Huard 2024-11-19，12:15

Q1.png

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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Answer 1

John D'Errico 2024-4-9

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https://ww2.mathworks.cn/matlabcentral/answers/2104946-lognormal-distribution-parameters-mu-and-sigma#answer_1438921

编辑：John D'Errico 2024-4-9

在 MATLAB Online 中打开

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
 LOGNRND Random arrays from the lognormal distribution.
    R = LOGNRND(MU,SIGMA) returns an array of random numbers generated from 
    the lognormal distribution with parameters MU and SIGMA.  MU and SIGMA 
    are the mean and standard deviation, respectively, of the associated 
    normal distribution.  The size of R is the common size of MU and SIGMA 
    if both are arrays.  If either parameter is a scalar, the size of R is 
    the size of the other parameter.
 
    R = LOGNRND(MU,SIGMA,M,N,...) or R = LOGNRND(MU,SIGMA,[M,N,...])
    returns an M-by-N-by-... array.
 
    The mean and variance of a lognormal random variable with parameters MU
    and SIGMA are
 
       M = exp(MU + SIGMA^2/2)
       V = exp(2*MU + SIGMA^2) * (exp(SIGMA^2) - 1)
 
    Therefore, to generate data from a lognormal distribution with mean M and
    Variance V, use
 
       MU = log(M^2 / sqrt(V+M^2))
       SIGMA = sqrt(log(V/M^2 + 1))
 
    See also LOGNCDF, LOGNFIT, LOGNINV, LOGNLIKE, LOGNPDF, LOGNSTAT, 
    RANDOM, RANDN.

    Documentation for lognrnd
       doc 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))
MU = 0.6628
SIGMA = sqrt(log(V/M^2 + 1))
SIGMA = 0.2462
X = lognrnd(MU,SIGMA,[1e8,1]);
mean(X)
ans = 2.0001
std(X)
ans = 0.5000