Hi Amitava, thanks for your feedback and apologies for the delay in responding. I have updated the article to include the equation for estimating alpha for the NB1 model.

If you do not want to go to the trouble of running the aux-regressions manually, you can use statsmodels's built in class for NB called NegativeBinomial() will estimate the alpha as part of the model fitting exercise.

Incidentally, you might notice that I have made a correction to the estimator of alpha for the NB2 in the updated version of the article.

'best!