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 ...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.展开更多
In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed...In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed the implication of the conditions in previous papers.Then we apply these consequences to B-valued random variables,and greatly improve the original results of the strong convergence of the general Jamison weighted sum.Furthermore,our discussions are useful to the corresponding questions of real-valued random variables.展开更多
基金Supported by the National Natural Science Foundation of China (No.10071081) & Special Foundation of USTC.
文摘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.
基金Research supported by National Science Foundation of China(No.10071081)special financial support of Chinese Academy of Sciences
文摘In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed the implication of the conditions in previous papers.Then we apply these consequences to B-valued random variables,and greatly improve the original results of the strong convergence of the general Jamison weighted sum.Furthermore,our discussions are useful to the corresponding questions of real-valued random variables.
