Optimization, MLE

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Optimization, MLE


I am a lerner in Stata and have some major problems replicating results from a paper.

The Lagrangian was differentated and reformulatet, gives:

(ni. - nii)/(1-pi) +(n.i - nii)/(pi) +lamda = 0 für alle i = 1,...,20

and Sum (pi) =1

n.i = sum row
ni. = sum column
nii = diagonal entries
Pii = cell-percentage of row-sum

I now want to solve this for the Pi's, if possible using MLE. But i just dont get how to specifie the commands.

For every kind of help i would be very grateful... I need to do this estimation for my bachelor thesis and i cant find help anywhere... Thank you very much in advance

Here i add the part of the paper i want to replicate :