I am trying to better understand the connection between the power law distribution and Zipf's distribution (law). There is a neat explanation in .
The article suggests that as we can derivate the power law function from Pareto's law, combined with the relationship between Pareto's law and Zipf's law, the power law parameter alpha is 1 + 1/b. From my understand, this would mean that we can directly determine Zipf's law's b parameter by simply having the power law alpha parameter. So e.g., an alpha of 2 would lead to a b of 1.
Is this true? So can I calculate alpha by e.g., using the methods by Clauset et al.  on my data and then directly determine the Zipf parameter b by the definition? This would allow me to use the exact methods by Clauset instead of the non-exact methods like fitting a straight line on a log-log plot. So I would also overcome the necessity of producing rankings etc.