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You can't use a goodness of fit test to claim that your data follows a power law (or any distribution). You can only use a GoF test (such as Kolmogorov-Smirnov)
by clircle 9y ago
You can't use a goodness of fit test to claim that your data follows a power law (or any distribution). You can only use a GoF test (such as Kolmogorov-Smirnov) to collect evidence that your data don't follow some hypothesized distribution. And if you collect enough data, your GoF test will reject every hypothesized distribution.
- hexane360 9y agoThat'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.