IMPROVEMENT ON THE TEST IN THE EXPONENTIAL FAMILY

作     者：ZHENG Zhongguo Peking University, Beijing 100871, China 

作者机构：北京大学 北京 

出 版 物：《Systems Science and Mathematical Sciences》 (系统科学与复杂性学报(英文版))

年 卷 期：1993年第6卷第2期

页      面：137-144页

核心收录：

学科分类：0711[理学-系统科学] 12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 08[工学] 0811[工学-控制科学与工程] 081103[工学-系统工程] 

基　　金：Supported by the NSFC and the Doctoral Programm Foundation of China 

主　　题：Exponential distribution best improvement of test 

摘      要：Let x1,…, xn be the life spans of n items. Suppose that we start the experi-ment at the time t=0 for all the items simultaneuously aud stop the experiment at the timet=r, where r is a stopping time. The observed data set is Zn=(x1,…, xk, r（x）),where xi（i=1,…, n） is the order statistic of xi, i=1,…, n and k=k（x） is the num-ber of the observed data. Suppose that the distribution family of xi, i=1,…, n is *** with life expectation θ0. For testing the hypothesis H0: θ≤θ0 againstH1: θθ0, we use the total time of experiment Sr=sub from i=1 to k xi +（n-k）r （x） as the teststatistic. We reject H0 as large value of Sr is observed. In this paper for a given stoppingtime r we construct a stopping time ro so that the resulting test is a best improvement ofthe one, which is based on r, in the sense that the power functions of the two tests are thesame but the test based on r0 is the one which has the minimnm total experiment time.