Relations and identities for the moments of order statistics from a sample containing a single outlier

In this paper, we derive several new recurrence relations and indentities satisfied by the single and the product moments of order statistics from a sample of size n in the presence of an outlier. These recurrence relations involve the first two single moments and the product moments in samples of sized n?1 and less. By making use of these recurrence relations we show that it is sufficient to evaluate at most two single rerents and (n?2)/2 product moment when n is even and two single moments and (n?2)/2 product moments when n is odd, in order to evaluate the first and second single moments and product moments of all order statistics in a sample of size n comprising an outlier, given these moments for the all sample of size less than n. These generalize the results of Govindarajulu (1963), Joshi (1971), and Joshi and Balakrishnan (1982) to the case when the sample includes a single outlier. We also establish some simple identitites involving linear combination of convariances of order statistics. These results can be effectively used to reduce the amount of numerical computation considerably and also to check the accuracy of the computations while evaluating means, variances and covariances of order statistics from an outlier model.     

有限群的弱拟正规子群

引入新概念--弱拟正规,并运用它探讨了偶数阶的QCLT-群;permutizer条件下的超可解性;以及可解群、超可解群,*-群和CLT-群等.     

模的矩阵表示与环的Morita结构

本文给出了模的矩阵表示，进而研究了环的 Ｍｏｒｉｔａ结构，主要结果： Ｒ为投射自由环当且仅当Ｒ上非零幂等矩阵具有特征根为１的特征向量。Ｒ为连通环当且仅当■Ｓ≈Ｋ_(０)Ｒ，存在生成子Ｐ∈Ｐ（Ｓ），使得 Ｋ_(０)Ｓ■ ≈ Ｚ， ■（［Ｐ］）＝１。     

经济增长、物价稳定双目标驱动下货币政策最优控制研究

经济增长与物价稳定始终是《中华人民共和国中国人民银行法》所规定货币政策的法定目标。“十三五”时期,中国政府一直坚持通过货币政策精准实现GDP增长与CPI稳定。基于1985—2019年GDP增长率与CPI时间序列数据估计了2020年CPI目标值,建立了我国GDP与CPI的二次线性型最优控制（LQOC）模型。研究发现,“十三五”时期我国GDP预期平均6.5%增速下的CPI为2.77%。利用该结果,对“十四五”规划期间货币政策最优轨迹进行模拟分析,结果显示,要实现“十四五”时期GDP与CPI的预期目标,在坚持稳健货币政策基调的同时,货币政策可以适度宽松,尤其是可以与财政政策积极耦合互动。研究结论有利于提高未来国民经济规划的实现率和精准度,亦能适时完善“十四五”规划的跨周期调节工具体系。