Abstract: The behavior of the generalized regular variation functions is studied. The properties of the Π and Γ variation functions are generalized to the generalized regular variation functions and their inverse functions-Γ(γ, b) functions. Γ(γ, b) functions' basic properties, expression theorem and equivalent conditions are proved. The domains of the extreme value distributions and rates of the convergence of the Von. Mises' condition are discussed.

Key words: generalized regular variation function, Γ(γ, b) function, domain of the extreme value distribution, Von.mises' condition

摘要： 讨论了广义正规变化函数的逆函数Γ(γ, b)，将Π变化函数及其逆--Γ变化函数的性质推广到广义正规变化函数及其逆函数Γ(γ, b)上，导出Γ(γ, b)的基本性质及表示定理和等价条件，利用所得结果讨论了极值分布的吸引场及Von Mises条件的收敛速度问题。

关键词: 广义正规变化函数, Γ(γ, b)变化函数, 极值分布吸引场, Von.Mises条件