What's the difference between ks test and bootstrap_p for power law fitting?

Question

I want to know the goodness of fit while fitting a power law distribution in R using poweRlaw package. After estimate_xmin() , I had a p-value 0.04614726. But the bootstrap_p() returns another p-value 0. So why do these two p-value differ? And how can I judge if it is a power law distribution? here is the plot when using poweRlaw for fittingpoweRlaw fitting result

Answer 1

You're getting a bit confused. One of the statistics that estimate_xmin returns is the Kolmogorov-Smirnoff statistic (as described in Clauset, Shalizi, Newman (2009)). This statistic is used to estimate the best cut-off value for your model, i.e. xmin. However, this doesn't tell you anything about the model fit.

To assess model suitability is where the bootstrap function comes in.