Tests of fit for the Rayleigh distribution based on the empirical Laplace transform

In this paper a class of goodness-of-fit tests for the Rayleigh distribution is proposed. The tests are based on a weighted integral involving the empirical Laplace transform. The consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated. As the decay of the weight function tends to infinity the test statistics approach limit values. In a particular case the resulting limit statistic is related to the first nonzero component of Neyman’s smooth test for this distribution. The new tests are compared with other omnibus tests for the Rayleigh distribution.     

Rational Functions with Prescribed Global and Local Minimizers

A family of multivariate rational functions is constructed. It has strong local minimizers with prescribed function values at prescribed positions. While there might be additional local minima, such minima cannot be global. A second family of multivariate rational functions is given, having prescribed global minimizers and prescribed interpolating data.     

Tensile Characterization of FRP Rods for Reinforced Concrete Structures

The application of FRP rods as an internal or external reinforcement in new or damaged concrete structures is based on the development of design equations that take into account the mechanical properties of FRP material systems.The measurement of mechanical characteristics of FRP requires a special anchoring and protocol, since it is well known that these characteristics depend on the direction and content of fibers. In this study, an effective tensile test method is described for the mechanical characterization of FRP rods. Twelve types of glass and carbon FRP specimens with different sizes and surface characteristics were tested to validate the procedure proposed. In all, 79 tensile tests were performed, and the results obtained are discussed in this paper. Recommendations are given for specimen preparation and test setup in order to facilitate the further investigation and standardization of the FRP rods used in civil engineering.     

在非线性回归模型中误差为AR(2)的相关性检验

本文讨论了在非线性回归模型中误差为AR(2)的相关性检验，得到了误差相关性检验的似然比检验统计量、Score检验统计量．对感兴趣参数和多余参数，利用Cox and Reid(1987)提出的正交化方法，给出了修正的似然比检验统计量和Score检验统计量．推广了胡跃清，韦博成(1994)讨论的在非线性回归模型中误差为AR(1)相关性检验的结果．     

试题质量评价研究

教学过程的规范化管理是保证教学质量的重要手段。考试是对教和学的效果的检验，是教学过程管理规范化必须要解决的问题，一直受到教学管理部门的重视，采取了多项措施解决有关问题，其中一个重要的手段是采用试题库。在采用试题库时，必须要有高质量的试题作保证。本探讨基于KDD技术的试题质量评价方法和指标，并通过实例来说明其有效性。     

Bayesian sequential reliability for Weibull and related distributions

Assume that the probability density function for the lifetime of a newly designed product has the form: [H(t)/Q()] exp{–H(t)/Q()}. The Exponential(), Rayleigh, WeibullW(, ) and Pareto pdf's are special cases.Q() will be assumed to have an inverse Gamma prior. Assume thatm independent products are to be tested with replacement. A Bayesian Sequential Reliability Demonstration Testing plan is used to eigher accept the product and start formal production, or reject the product for reengineering. The test criterion is the intersection of two goals, a minimal goal to begin production and a mature product goal. The exact values of various risks and the distribution of total number of failures are evaluated. Based on a result about a Poisson process, the expected stopping time for the exponential failure time is also found. Included in these risks and expected stopping times are frequentist versions, thereof, so that the results also provide frequentist answers for a class of interesting stopping rules.This research was supported by NSF grants DMS-8703620 and DMS-8923071, and forms part of the Ph.D. Thesis of the first author, the development of which was supported in part by a David Ross grant at Purdue University. The authors thank the editors and a referee for insightful comments and suggestions.     

应用Hotelling T~2检验评价学生学习成绩的探讨

本文简述了ＨｏｔｅｌｌｉｎｇＴ２检验法，并应用该法对某校学生的学习成绩进行了分析评价，发现其效果较为满意。认为对多变量资料进行分析评价需用ＨｏｔｅｌｌｉｎｇＴ２检验。     

泛函梯度数值计算的一种新方法—正交试验法

本文研究并揭示了L_(2~a)(2~(2~a-1))型正交表行(列)间的递推规律,提出了一种泛函梯度数值计算的新方法——正交试验法,该方法在计算速度和精度上优于直接梯度法;在通用性及节省内存方面优于伴随算子法。     

A bartlett-type adjustment for the likelihood ratio statistic with an ordered alternative

For testing the equality of normal variances with an increasing alternative, under the null hypothesis the likelihood ratio test statistic is asymptotically distributed as a mixture of chi-squared distributions. In this paper a Bartlett-type adjustment is proposed to improve the approximation of the null distribution of the likelihood ratio test statistic with an ordered alternative.     

Tests of ordered hypotheses in linkage in heredity

The asymptotic null distribution of the likelihood ratio test for two cases of ordered hypotheses in a particular genetic model is considered. A simple iterative process is proposed in order to get the restricted estimates. It is shown that both tests have asymptotically a chi-bar squared distribution and the same size. A simulation study is also conducted in order to compare the usual unrestricted test with the corresponding one of ordered hypotheses. Finally, the results are extended to some special cases.