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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:
60E05 Probability distributions: general theory
62E99 Statistical distribution theory
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