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

June 23rd, 2021, 2:35 pm

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

June 24th, 2021, 4:07 am

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

June 28th, 2021, 11:32 am

I see. Thank  you so much.