The least concave majorant of the empirical distribution function

The author compares two estimators of a continuous, concave distribution function having support on the positive half line. In terms of samples from uniform distributions, he gives stochastic bounds for the pointwise and sup‐norm differences between the least concave majorant of the empirical distribution function and the underlying distribution function. He also offers evidence demonstrating the almost paradoxical result that the empirical distribution function is not as good an estimator as its least concave majorant in terms of sup‐norm error but a better pointwise estimator of the true distribution function in terms of mean squared error.     

关于曲线拐点的定义及判别法

通过对不同教材中拐点定义进行比较、分析,给出了拐点较为恰当的定义,并在此基础上给出了拐点的三个新的判别定理.     

钢结合金的性能特点及其在模具上的应用

概述了新型工程材料钢结合金的物理机械性能特点和工艺性能特点 ,介绍了钢结合金在模具工业中的使用效果 ,指出该材料对机电行业发展的影响     

Analysis of Order Statistics from Distributions with Regularly Varying Tails

In this article, necessary conditions for comparing order statistics from distributions with regularly varying tails are discussed in terms of various stochastic orders. A necessary and sufficient condition for stochastically comparing tail behaviors of order statistics is derived. The main results generalize and recover some results in Kleiber (2002 Kleiber, C. (2002). Variability ordering of heavy-tailed distributions with applications to order statistics. Statist. Probab. Lett. 58:381388.[Crossref], [Web of Science ®] , [Google Scholar], 2004 Kleiber, C. (2004). Lorenz ordering of order statistics from log-logistic and related distributions. J. Statist. Plann. Infer. 120:2004.[Crossref], [Web of Science ®] , [Google Scholar]). Extensions to coherent systems are mentioned as well.     

Optimal Reinsurance Under VaR and CTE Risk Measures When Ceded Loss Function is Concave

Cai et al. (2008 Cai, J., Tan, K.S., Weng, C.G., Zhang, Y. (2008). Optimal reinsurance under VaR and CTE risk measures. Insur. Math. Econ. 43(1):185–196.[Crossref], [Web of Science ®] , [Google Scholar]) explored the optimal reinsurance designs among the class of increasing convex reinsurance treaties under VaR and CTE risk measures. However, reinsurance contracts always involve a limit on the ceded loss function in practice, and thus it may not be enough to confine the analysis to the class of convex functions only. The object of this article is to present an optimal reinsurance policy under VaR and CTE optimization criteria when the ceded loss function is in a class of increasing concave functions and the reinsurance premium is determined by the expected value principle. The outcomes reveal that the optimal form and amount of reinsurance depend on the confidence level p for the risk measure and the safety loading θ for the reinsurance premium. It is shown that under the VaR optimization criterion, the quota-share reinsurance with a policy limit is optima, while the full reinsurance with a policy limit is optima under CTE optimization criterion. Some illustrative examples are provided.     

Correlation between the numbers of two types of children in a family with the mpsd for the family size

The family size (sibship size) N is regarded as an integer-valued random variable having a Modified Power Series distribution (MPSD) of Gupta (1974). The family produces two types of children, with probabilities p and q (p+q =1) . It is proved that the correlation between the numbers B and C of these children is positive or negative according as the function log f(θ) is convex or concave with respect to the function g(θ), (see Section 2). This condition is a simple and a natural extension of the one given by Rao et al (1973). Several examples are discussed to illustrate the result.     

紫姬与黛玉：心理异变与死亡意志

紫姬与黛玉是受东方封建伦理道德制度残害的两位女性。她们固有的反抗意志与现实压迫产生了强烈的矛盾冲突,导致她们正常的心理扭曲、异变和趋于无悔的死志。     

Testing for equivalence of variances using Hartley's ratio

Hartley's test for homogeneity of k normal‐distribution variances is based on the ratio between the maximum sample variance and the minimum sample variance. In this paper, the author uses the same statistic to test for equivalence of k variances. Equivalence is defined in terms of the ratio between the maximum and minimum population variances, and one concludes equivalence when Hartley's ratio is small. Exact critical values for this test are obtained by using an integral expression for the power function and some theoretical results about the power function. These exact critical values are available both when sample sizes are equal and when sample sizes are unequal. One related result in the paper is that Hartley's test for homogeneity of variances is no longer unbiased when the sample sizes are unequal. The Canadian Journal of Statistics 38: 647–664; 2010 © 2010 Statistical Society of Canada     

"模具生产管理与营销"课程教学方法探讨

文章介绍了"模具生产管理与营销"课程在教学过程中所应用到的多媒体教学、案例分析、参与型教学等教学方法,并对它们之间的关系作了进一步的探讨。     

纳西族殉情现象及其社会心理原因分析

在20世纪50年代以前的丽江纳西族社会里,殉情是个非常突出的现象,以至于外人把丽江称为"殉情之都"。丽江纳西族的殉情之风有深刻的社会、宗教、文化、心理原因。殉情是改土归流后严格的包办婚制与原有的自由婚剧烈冲突的产物;为殉情者提供理想乐园是纳西族原始宗教对情死者的同情和安排;殉情这种极端做法源于封建礼教在丽江的盛行和严格规范带来的社会谴责和自我谴责压力。如今,社会制度的转变消灭了殉情现象,但在一个民族中曾经出现过的悲剧现象,仍是研究这个民族民族性的重要方面。