That's where #6 comes in: >Use Vuong's test to check alternatives, and be prepared for disappointment. Even if you've estimated the parameters of your paramete

That's where #6 comes in: >Use Vuong's test to check alternatives, and be prepared for disappointment. Even if you've estimated the parameters of your parameters properly, and the fit is decent, you're not done yet. You also need to see whether other, non-power-law distributions could have produced the data. This is a model selection problem, with the complication that possibly neither the power law nor the alternative you're looking at is exactly right; in that case you'd at least like to know which one is closer to the truth.