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EdisonCruise
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Posts: 122
Joined: September 15th, 2012, 4:22 am

### Is it necessary to piecewisely fit power-law distribution in empirical data?

In AARON CLAUSET’s paper power-law distributions in empirical data: ‘’In practice, few empirical phenomena obey power laws for all values of x. More often the power law applies only for values greater than some minimum x_min. In such cases we say that the tail of the distribution follows a power law.”

So for the data x<x_min, is it necessary to fit with another distribution? If so, the probability density function becomes piecewise and what functions are usually used in such a case? The part x<x_min is about 95% of my data. I find few literature for this problem.

Alan
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Joined: December 19th, 2001, 4:01 am
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### Re: Is it necessary to piecewisely fit power-law distribution in empirical data?

Not necessarily. You can cook up a density that smoothly transitions from a pure power in the tail to something else. For the case at hand, apparently on the positive axis, say
$C (a^2 + x^2)^{-b}$ or a zillion other choices

EdisonCruise
Topic Author
Posts: 122
Joined: September 15th, 2012, 4:22 am

### Re: Is it necessary to piecewisely fit power-law distribution in empirical data?

I see. Thank  you so much.