摘要
给定随机变量X,Y,Z,针对它们之间可能出现的大小关系X<Y<Z,研究该情形发生概率的估计问题,即有关P(X<Y<Z)的估计.作了两方面工作:(1)当X,Y,Z分布已知时,推导出P(X<Y<Z)的表达式,利用极大似然估计以及渐近分布的性质,得到P(X<Y<Z)的极大似然估计和区间估计;(2)当X,Y,Z分布未知时,利用经验似然比以及非参数Wilks定理,得到P(X<Y<Z)的极大经验似然估计和经验置信域.
Given random variables X, Y and Z, for the probably occurred relationship among them：X〈Y〈Z , we research the estimate of its probability, i.e. the P（X〈Y〈Z）. The article contains two parts： 1） when the distributions of X,Y and Z of are known, based on the proper- ties of MLE （maximum likelihood estimate） and asymptotic distribution, we deduce the expres- sion of P（X〈Y〈Z） and derive the maximum likelihood estimate and interval estimate 2）when the distributions of X,Y and Z are unknown, depends on ELR（empirical likelihood ratio） and nonparametric Wilkrs theorem, we deduce the maximum empirical likelihood estimate and empiri- cal confidence band.
出处
《山东理工大学学报（自然科学版）》
CAS
2014年第2期34-39,共6页
Journal of Shandong University of Technology:Natural Science Edition
关键词
极大似然估计
区间估计
渐近分布
经验似然比
maximum likelihood estimate interval estimate asymptotic distribution empiricallikelihood ratio
