广义经验分布函数及其性质

GENERALIZED EMPIRICAL DISTRIBUTIONFUNCTION AND IT'S PROPERTIES

本文将经验分布函数推广到更一般的形式，称为广义经验分布函数．虽然广义经验分布函数已不再具有用频率估计概率的性质，但作为未知总体分布函数的估计量，它仍具有许多良好的渐近性质．本文还讨论了它的小样本性质和Ｂｏｏｔｓｔｒａｐ逼近的相合性．

In this note, the classical empirical distribution function is generalized. Although the generalized empirical distribution function has no longer the frequency characteristic, as an estimator of the population distribution function, it has many nice asymptolic properties. The small sample properties and the consistence of the Bootstrap aproximation are also discussed.