On a class exhibiting trend change in average failure rate

Abstract

Weak convergence and moment convergence issues are investigated for the New Better than Average Failure Rate (NBAFR) family (introduced by Loh (1984 Loh, W. Y. 1984. A new generalization of the class of NBU distributions. IEEE Transactions on Reliability R-33 :97–113[Crossref], [Web of Science ®] , [Google Scholar])). We explore the validity of these results in the context of a more general ageing class that we introduce. We prove some new properties of this class and derive its interrelationships with other non-monotonic ageing families. Reliability and moment bounds are obtained and an interesting characterization of exponentiality is proved. Special cases of our results lead to new theorems for the NBAFR class. Finally weak convergence and related issues are established for this class.     

Visualization of generalized mean estimators using auxiliary information in survey sampling

Abstract

The mean estimators with ratio depend on multiple auxiliary variables and unknown parameters in a finite population setting. We propose a new generalized approach with matrices for modeling the mutivariate mean estimators with two auxiliary variables. Our approach brings naturally a graphical analysis for comparing mean estimators.     

Using local linear kernel smoothers to test the lack of fit of nonlinear regression models

Herein, we propose a data-driven test that assesses the lack of fit of nonlinear regression models. The comparison of local linear kernel and parametric fits is the basis of this test, and specific boundary-corrected kernels are not needed at the boundary when local linear fitting is used. Under the parametric null model, the asymptotically optimal bandwidth can be used for bandwidth selection. This selection method leads to the data-driven test that has a limiting normal distribution under the null hypothesis and is consistent against any fixed alternative. The finite-sample property of the proposed data-driven test is illustrated, and the power of the test is compared with that of some existing tests via simulation studies. We illustrate the practicality of the proposed test by using two data sets.     

Kernel Estimation of Rate Function for Recurrent Event Data

Abstract.  Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce a curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.     

模糊技术在高校教学评估中的研究

研究了高校教学评估中知识的模糊关系及权重问题,讨论在有关模糊隶属函数计算方法的基础上,将模糊技术应用在教学评估中,为教学评估的研究提供一条新的途径。     

指数级数的增长性和值分布

本文研究了随机狄里克莱级数 在随机变量序列{Xn}独立（可不同分布）以及满足等条件时的增长性以及值分布,得到了一些新的结果.     

一类带有分布参数系统的最佳控制

本文给出一类非均匀弦的横向振动的最佳控制，推广了P C Park的结果。这一结果同样适用于同类型振动问题。     

日语中的委婉表现及其语用功能

日语里有很多委婉的表现形式 ,如改换词语、以表喻里的暗喻法、模糊语、省略、正话反说、反话正说、借用其他词语等等。不同的表现形式包含有不同的语用功能。采用这些委婉的表现形式 ,其目的都是为了最终达到理想的交际效果。     

浅谈中小学合唱教学

本文通过对童声合唱艺术的重要性与训练中若干技术问题的分析 ,结合我国中小学音乐教育的实际状况而进行思考 ,认为在我国中小学音乐教育中 ,合唱教学应该占据与其地位相适应的位置 ;在合唱教学的具体实施中 ,要让中小学学生在曲目上有多样性的选择空间 ,以适应其生理与心理特点 ;学生所学的音乐知识应在合唱训练中得到全面的实践 ,从而使学生的艺术修养得到全面提升