Approximation of the Bivariate Renewal Function

Recently, Kambo and his co-researchers (2012) proposed a method of approximation for evaluating the one-dimensional renewal function based on the first three moments. Their method is simple and elegant, which gives exact values for well-known distributions. In this article, we propose an analogous method for the evaluation of bivariate renewal function based on the first two moments of the variables and their joint moment. The proposed method yields exact results for certain widely used bivariate distributions like bivariate exponential distribution, bivariate Weibull distributions, and bivariate Pareto distributions. An illustrative example in the form of a two-dimensional warranty problem is considered and comparisons of our method are made with the results of other models.     

Inferences on the Means of Two Log-Normal Distributions: A Computational Approach Test

In this article, we propose a novel approach for testing the equality of two log-normal populations using a computational approach test (CAT) that does not require explicit knowledge of the sampling distribution of the test statistic. Simulation studies demonstrate that the proposed approach can perform hypothesis testing with satisfying actual size even at small sample sizes. Overall, it is superior to other existing methods. Also, a CAT is proposed for testing about reliability of two log-normal populations when the means are the same. Simulations show that the actual size of this new approach is close to nominal level and better than the score test. At the end, the proposed methods are illustrated using two examples.     

疲劳裂纹扩展试验裂纹图像采集系统

针对目前金属疲劳裂纹扩展检测方法存在效率低、操作繁琐、精度不高，不能实现实时性等缺点，文章提出了基 于机器视觉的裂纹检测方法。根据金属疲劳裂纹扩展试验过程中裂纹图像的采集要求，设计了摄像头位置可自动调整 的疲劳裂纹图像采集系统，包括摄像头安装运动装置，裂纹图像采集装置以及摄像头运动控制系统。图像采集装置由高 分辨率黑白面阵CCD摄像头、光学镜头，光源照明装置和图像采集卡组成，前3者安装在摄像头支架上，与摄像头运动 装置相连。摄像头运动装置中的X，Y，，Z轴运动机构由步进电机带动滚珠导轨机构。在基于ARM技术的运动控制系统 的控制下摄像头可沿X，Y，，Z轴作高精度直线运动，实现和试件之间精确位置的调整。实验结果表明，所设计的系统可 采集到疲劳裂纹扩展试验过程中高清晰度、高分辨率的试件裂纹图像，满足下一步裂绞尺寸计算的要求；摄像头运动定 位精度可达到0. 02 mm，满足精确的系统聚焦、位置调整、跟踪采集的要求。     

国家级教学名师的优秀品质及其养成

通过对5位国家级教学名师的自述报告进行三级编码和主题凝练，研究发现国家级教学名师作为教师队伍的杰出代表，在其专业发展过程中养成了许多优秀品质。例如：教学方面注重实践、考虑周全，师德方面以德施教、追求卓越，科研方面以教带研、实现创新。国家级教学名师优秀品质的养成通常经历了漫长而曲折的过程，不仅需要精神与物质力量的共同推动，还需要家庭、学校和社会各环境要素的相互促进，以及社会取向养成方式和个人取向养成方式的互相配合。深入探究国家级教学名师的优秀品质及其养成之道，可以为教师专业发展提供借鉴与启示。     

巴渝古崖居的空间分布与景观特征

巴渝古崖居的分布与地理、地质、交通等诸多因素有关，以成渝交通要道、长江干流和支流为线，串起沿途各个点，由线成面，呈现出渝西、渝东北两头集中、整体北多南少的分布特征。巴渝古崖居大多开凿于明清晚期，这一时期巴渝许多地区战乱频繁、匪患猖獗。古崖居的集中分布与这些地区相吻合，从侧面印证了巴渝古崖居的空间分布特征。巴渝古崖居的广泛开凿体现了古人高超的建筑艺术以及社会历史文化的变迁。     

A new generalized Weibull distribution in income economic inequality curves

Researchers have been developing various extensions and modified forms of the Weibull distribution to enhance its capability for modeling and fitting different data sets. In this note, we investigate the potential usefulness of the new modification to the standard Weibull distribution called odd Weibull distribution in income economic inequality studies. Some mathematical and statistical properties of this model are proposed. We obtain explicit expressions for the first incomplete moment, quantile function, Lorenz and Zenga curves and related inequality indices. In addition to the well-known stochastic order based on Lorenz curve, the stochastic order based on Zenga curve is considered. Since the new generalized Weibull distribution seems to be suitable to model wealth, financial, actuarial and especially income distributions, these findings are fundamental in the understanding of how parameter values are related to inequality. Also, the estimation of parameters by maximum likelihood and moment methods is discussed. Finally, this distribution has been fitted to United States and Austrian income data sets and has been found to fit remarkably well in compare with the other widely used income models.     

Inference and optimal design of multiple constant-stress testing for generalized half-normal distribution under type-II progressive censoring

The generalized half-normal (GHN) distribution and progressive type-II censoring are considered in this article for studying some statistical inferences of constant-stress accelerated life testing. The EM algorithm is considered to calculate the maximum likelihood estimates. Fisher information matrix is formed depending on the missing information law and it is utilized for structuring the asymptomatic confidence intervals. Further, interval estimation is discussed through bootstrap intervals. The Tierney and Kadane method, importance sampling procedure and Metropolis-Hastings algorithm are utilized to compute Bayesian estimates. Furthermore, predictive estimates for censored data and the related prediction intervals are obtained. We consider three optimality criteria to find out the optimal stress level. A real data set is used to illustrate the importance of GHN distribution as an alternative lifetime model for well-known distributions. Finally, a simulation study is provided with discussion.     

基于遗传算法的装备采购决策优化研究

在装备采购中，由于需求单位地域分布和担负的任务各不相同，对装备的品种、数量、时限要求也就不一样，如何使装备采购科学化、合理化，是一个涉及多变量、多目标的复杂系统问题。在综合考虑装备采购各项因素的基础上，构建多约束条件下的多目标模糊指派模型，提出了基于遗传算法的解决方案，最后通过案例进行仿真实验，验证该算法的可行性和有效性，解决了采用传统优化方法难以解决的装备采购优化决策问题。     

Confidence intervals,significance values,maximum likelihood estimates,etc. sharpened into Occam’s razors

Abstract

Confidence sets, p values, maximum likelihood estimates, and other results of non-Bayesian statistical methods may be adjusted to favor sampling distributions that are simple compared to others in the parametric family. The adjustments are derived from a prior likelihood function previously used to adjust posterior distributions.