Characterizations on Heavy-tailed Distributions by Means of Hazard Rate  

作　　者：ChunSu Qi-heTang 

机构地区：[1]DepartmentofStatisticsandFinance,UniversityofScienceandTechnologyofChina,Hefei230026,China [2]DepartmentofQuantitativeEconomics,UniversityofAmesterdam,Roetersstraat11,1018WBAmsterdam,Netherland

出　　处：《Acta Mathematicae Applicatae Sinica》2003年第1期135-142,共8页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No.10071081) & Special Foundation of USTC.

摘　　要：Abstract Let F(x) be a distribution function supported on [0,X), with an equilibrium distribution function Fe(x). In this paper we shall study the function $r_e(x)( - {\rm ln}{\overline F}_e ( x ))\prime = {\overline F}( x )/\int_x^\infty {\overline F}( u )du $, which is called the equilibrium hazard rate of F. By the limiting behavior of re(x) we give a criterion to identify F to be heavy-tailed or light-tailed. Two broad classes of heavy-tailed distributions are also introduced and studied.Abstract Let F(x) be a distribution function supported on [0,X), with an equilibrium distribution function Fe(x). In this paper we shall study the function $r_e(x)( - {\rm ln}{\overline F}_e ( x ))\prime = {\overline F}( x )/\int_x^\infty {\overline F}( u )du $, which is called the equilibrium hazard rate of F. By the limiting behavior of re(x) we give a criterion to identify F to be heavy-tailed or light-tailed. Two broad classes of heavy-tailed distributions are also introduced and studied.

关 键 词：Keywords Equilibrium distribution Hazard rate heavy-tailed distribution. 

分 类 号：O211.3[理学—概率论与数理统计]