- Two Sided Tests (Null hypothesis is that both distributions are equally far from the "truth"):
- Fail to reject null hypothesis for power-law and log-normal.
- Reject the null hypothesis for the Weibull.
- Reject the null hypothesis for the exponential.
- One-sided Tests (Null hypothesis is a power-law):
- Fail to reject the null hypothesis of power-law compared with Weibull.
- Fail to reject the null hypothesis of a power-law compared with an exponential.
- Vuong LR test for nested-models (used only for comparing a power-law and a power-law w/ exponential cut-off):
- Reject null hypothesis of a power-law in favor of a power-law with exponential cut-off.

**Power-law with exponential cut-off: -2143.809**- Log-normal: -2144.513
- Power-law: -2146.368
- Weibull: -2173.089
- Exponential: -2182.766

I may have been a bit hasty in that conclusion. Upon further review, I think that there is either a bug in my code, or that I have made some conceptual error in implementing the test. For one, I certainly should have noticed that the p-values for both tests were suspiciously small (they were both 0.00!) given the difference in their respective LR of less than 1!

As always comments are very much encouraged...

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