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Is it possible for a distribution $F(x)$ that has not a Pareto ($G(x)$) right tail equivalence to fit well heavy-tailed data? That is, to have ${\lim_{x\rightarrow\infty}}\frac{1-F(x)}{1-G(x)}=0$ instead of ${\lim_{x\rightarrow\infty}}\frac{1-F(x)}{1-G(x)}>0$

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It depends on how you define "heavy-tailed data". For example, if you understand heavy tails as tails that are heavier than exponential (see wikipedia), then you can find heavy-tailed distributions with lighter tails than Pareto that satisfy your condition. That is, there are distributions that have tails heavier than exponential but lighter than any power (this is, Pareto). An example of such distributions is the Sinh-ArcSinh distribution:

http://biomet.oxfordjournals.org/content/96/4/761.abstract

In many cases these distributions may fit the data well.

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  • $\begingroup$ I use heavy-tailed= "heavier than exponential". Thank you for the reference, I will have a look at it. $\endgroup$ – Patricia Sep 26 '16 at 15:42

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