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Characterizations on heavy-tailed distributions by means of hazard rate. (English) Zbl 1043.60012
Summary: Let $$F(x)$$ be a distribution function supported on $$[0,\infty)$$, with an equilibrium distribution function $$F_e(x)$$. We study the function $r_e(x)= (-\ln \overline{F}_e(x))'= \overline{F}(x) \biggl/ \int_x^\infty \overline{F}(u)\, du,$ which is called the equilibrium hazard rate of $$F$$. By the limiting behavior of $$r_e(x)$$ we give a criterion to identify $$F$$ to be heavy-tailed or light-tailed. Two broad classes of hevy-tailed distributions are also introduced and studied.

##### MSC:
 6e+06 Probability distributions: general theory 6.2e+100 Statistical distribution theory
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##### References:
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