# Interpretation of lognormal parameters in Matlab

I have a couple of questions regarding the interpretation of the lognormal parameters in MATLAB, working towards modelling using a lognormal distribution. My interpretations of the various MATLAB functions are as follows. Are they correct?

The function "lognrnd" may be used to generate log normally distributed random variables. The mu and sigma parameters applied are the mean and standard deviation of the associated normal distribution.

The function "lognstat" converts the mean and SD of the associated normal distribution to the mean and SD of the lognormal distribution.

The function "lognfit" returns the mean and SD of the associated normal distribution of the input data.

When using 'mle' to fit the log normal distribution to given data (I am expanding the model, so use 'mle' after testing on lognfit), pdf_logfn = @(x, a, b) lognpdf(x, a, b)

The estimated parameters are also the mu and sigma of the associated normal distribution. In order to access the parameters of the lognormal distribution, lognstat can be used.

When reporting, would the lognormal parameters, i.e., after the conversion using lognstat be the ones to be reported, given the model consists of lognormal distribution?

Many thanks!

See answers in bold upper case embedded below. All are as per documentation.

The function "lognrnd" may be used to generate log normally distributed random variables. The mu and sigma parameters applied are the mean and standard deviation of the associated normal distribution. YES

The function "lognstat" converts the mean and SD of the associated normal distribution to the mean and SD of the lognormal distribution. YES

The function "lognfit" returns the mean and SD of the associated normal distribution of the input data. YES

When using 'mle' to fit the log normal distribution to given data (I am expanding the model, so use 'mle' after testing on lognfit), pdf_logfn = @(x, a, b) lognpdf(x, a, b) YES. INPUT AND OUTPUT OF ALL THESE MATLAB LOGNORMAL FUNCTIONS ARE IN TERMS OF THE PARAMETERS OF THE ASSOCIATED (UNDERLYING) NORMAL DISTRIBUTION.

The estimated parameters are also the mu and sigma of the associated normal distribution. In order to access the parameters of the lognormal distribution, lognstat can be used. YES. NOTE: CONVERSION FORMULAS ARE SHOWN AT https://www.mathworks.com/help/stats/lognpdf.html .

When reporting, would the lognormal parameters, i.e., after the conversion using lognstat be the ones to be reported, given the model consists of lognormal distribution? THIS IS A MATTER OF CONVENTION. I HAVE ASKED AUTHORS IN REAL-WORLD WHO DIDN'T KNOW WHETHER THEIR MEAN AND SIGMA WERE FOR THE ACTUAL LOGNORMNAL DISTRIBUTION OR THE PARAMETERS OF THE ASSOCIATED (UNDERLYING) NORMAL DISTRIBUTION. WHEN REPORTING, MAKE CLEAR WHAT YOU ARE REPORTING. YOU CAN EVEN REPORT IT BOTH WAYS.