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I want to find out if a given distribution follows a power law. My question is, can we use a qq plot to do this?

I first estimate the xmin by integrating over the entire dataset. Following which, I found alpha using MLE. (xmin and alpha are explained at the following link :- https://en.wikipedia.org/wiki/Power_law under the section Power-law probability distributions)

Next I plan to use a qqplot of the empirical distribution and theoretical distribution(with the computed alpha and xmin).

Am I on the right track ?

Also, what reference line( corresponding to qqline) should be used in the case of power law?

Also we can use a log log plot to find out if a distribution is following a power law. My query is, will the qqplot analysis augment the log log plot analysis ? Is it valid to do a qqplot analysis for a power law distribution?

Piyush Gupta
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  • There are many such questions on stat exhchange, see for ex. https://stats.stackexchange.com/questions/58220/what-distribution-does-my-data-follow/58241#58241 – user2974951 Oct 26 '18 at 10:11
  • Hi, thanks for replying. The link you provided explains the construction of lognormal qq plots. This is easy when we compare the current data to normal/lognormal since rescaling is possible. While in case of power law and Pareto distribution, no rescaling is possible using distribution mu and sigma. Therefore, what inference can we really draw if we get a straight line in case of a qq plot which has slope m≠1 ? – Piyush Gupta Nov 08 '18 at 07:18

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