fit_method and different outcomes in distribution_compare

[sanjasc...@gmail.com]

Hi Jeff,

I hope this is my last questions for a while.

When fitting the distribution to power law with fit_method='KS' and consequently evaluating with all available distributions in distribution_compare, the result is that none of them is a better fit to my data than powerlaw. 

However, if running with default fit_method='likelihood', then in some cases lognormal (or truncated_power_law) is strongly preferred distribution over powerlaw.  How should we interpret such different results? In particular, both fitting methods (KS and likelihood) find the same optimal alpha and xmins for my data -- so how come that distribution_compare results are then so different? 

Moreover, the different results happen only under xmin given by me, not the optimal calculated one. Concretely, for contrasting results, R and p are very similar scales, but R has negative sign when using likelihood method and positive with KS method. 

Many thanks!
Sanja

[Jeff Alstott]

Getting into different measures for fitting is confusing. In brief, the KS test is sensitive to certain arbitrary parts of the distribution, while maximum likelihood is sensitive to where most of the data is. Using anything other than maximum likelihood is probably not justified, but see the section "Maximum Likelihood and Independence Assumptions" from the paper: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0085777#s5

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[sanjasc...@gmail.com]

Hi again,

Thank you. Possible reason is that while lognormal is found a better fit for our data, it is not clear how realistic it is when it comes to our data. Namely, lognormal's parameter mu is negative and our distribution just counts number of objects present...

In any case, since this only happens when I try to use smaller xmin, it is ok to use xoptimal found by powerlaw and have power law fit for the tail of the data.

Cheers!

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