一个新的期望恒等式及其在正态预测势计算中的应用  

A New Expectation Identity and Its Application in the Calculations of Predictive Powers Assuming Normality

作　　者：张应应 荣腾中[1] 李曼曼[1] ZHANG Yingying;RONG Tengzhong;LI Manman(Department of Statistics and Actuarial Science,College of Mathematics and Statistics,Chongqing University,Chongqing,401331,China)

机构地区：[1]重庆大学数学与统计学院统计与精算学系,重庆401331

出　　处：《应用概率统计》2020年第5期523-535,共13页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the Fundamental Research Funds for the Central Universities (Grant Nos.2019CDXYST0016;2018CDXYST0024);the China Scholarship Council (Grant No.201606055028);the National Natural Science Foundation of China (Grant No.11671060);the MOE Project of Humanities and Social Sciences on the West and the Border Area (Grant Nos.20XJC910001;14XJC910001);Chongqing Key Laboratory of Analytic Mathematics and Applications

摘　　要：为了计算预测势,我们建议使用一个简洁的期望恒等式来直接计算期望值.我们计算了具有非零阈值的假设对五种不同类型的预测势,即具有经典势和贝叶斯势的非序贯试验,以及混合预测、贝叶斯预测和经典预测的序贯试验.此外,通过三个例子说明了各种预测势的计算.最后,在计算文献[9]中的平均成功概率时,很难找到预测势的预测分布,而利用期望恒等式进行计算是很简单的.For calculating the predictive powers,we suggest an elegant expectation identity to directly calculate the expectations.We calculate the predictive powers of the hypotheses with a nonzero threshold for five different categories,which are non-sequential trials with classical power and Bayesian power,and sequential trials with hybrid predictions,Bayesian predictions,and classical predictions.Moreover,the calculations of the various predictive powers are illustrated through three examples.Finally,when calculating the average success probability in[9],it is tricky to find the predictive distribution for the predictive power,whereas,it is straightforward to utilize the expectation identity for the calculation.

关 键 词：期望等式 预测势 正态模型 单边假设 平均成功概率 

分 类 号：O212[理学—概率论与数理统计] O213[理学—数学]