Given a dataset X with N observations in 11 dimensions, where each variable is restricted to be >= 0, how is it possible to fit an 11-dimensional log-normal distribution to this dataset?

I only found sources for fitting an univariate lognormal to data, but I didn't find anything for the multivariate case.

I would be happy if this was possible in MATLAB, however python or R would also be fine.

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#### Best Answer

It seems that based on the definition given by Bill Huber the multivariate lgonormal is given by taking a specified multivariate normal distribution $(Y_1,Y_2,…,Y_n)$ and then define the multivariate vector $(exp(Y_1),exp(Y_2),…,exp(Y_n))$ as a multivariate lognormal. So as Bill Huber suggests you can use the $ln$ of the vector that you observe to estimate the mean and covariance matrix of the multivariate normal (many choices for this) and that estimate defines the estimated multivariate lognormal.

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