Estimation of the location and scale parameters of the extreme value distmbution based on multiply type-II censored samples

In this paper, we consider the problem of estimating the location and scale parameters of an extreme value distribution based on multiply Type-II censored samples. We first describe the best linear unbiased estimators and the maximum likelihood estimators of these parameters. After observing that the best linear unbiased estimators need the construction of some tables for its coefficients and that the maximum likelihood estimators do not exist in an explicit algebraic form and hence need to be found by numerical methods, we develop approximate maximum likelihood estimators by appropriately approximating the likelihood equations. In addition to being simple explicit estimators, these estimators turn out to be nearly as efficient as the best linear unbiased estimators and the maximum likelihood estimators. Next, we derive the asymptotic variances and covariance of these estimators in terms of the first two single moments and the product moments of order statistics from the standard extreme value distribution. Finally, we present an example in order to illustrate all the methods of estimation of parameters discussed in this paper.     

Moments and generating functions for the absortion distribution and its negative binomial analogue

The moments of the absorption are difficult to obtain. The generating functions are basic hypergeometric functions. This paper shows how to define two shift operators that allow elementary arguments to be used to develop recursions for the expected values of general functions. The exact moments of the distribution follow. The generating function for the negative binomial analogue gives the moments directly.     

Approximations in a group sequential test with unequal group sizes

Our concern in this paper is a group sequential test design for which the sample sizes between interim analyses are not identical. First, we consider a repeated significance test for comparing two treatments in a clinical trial, and study asymptotic properties of the test statistic. Using the arguments developed by Siegmund (1985, Chapters 8 and 9), we then obtain approximations for the overall significance level of the test and for the error level at each interim analysis. Simulation studies are performed to assess the accuracy of the approximations and the robustness of the approximations are examined using numerical examples.     

An Approximate Normalizing Power Transformation for the FDistribution

A power transformation of the Fdistribution is presented, yielding simple normal approximations for both probabilities and quantiles of the distribution. The transformation proposed is shown to produce the well-known Wilson-Hilferty cube root transformation (Wilson and Hilferty, 1931) for the chi-square distribution as a limiting case, as well as the Fisher logarithmic transformation (Fisher, 1924, 1925) for equal degrees of freedom. A numerical assessment of the accuracy achieved for approximating tail probabilities and a comparison with some of the existing approximate procedures are given.     

Combining Univariate Tests for Multivariate Location Problem

In this article, three methods of combining dependent univariate tests are studied. The Bahadur approximate efficiencies are derived under the asymptotic normal assumption. These procedures are applied to the multivariate location problem and compared with two Hotelling-type tests. A Monte Carlo study indicates that in certain cases the powers of the combination methods are much better than Hotelling's T ² and other multivariate nonparametric tests.     

Analysis of hybrid censored competing risks data

In this paper, we consider the analysis of hybrid censored competing risks data, based on Cox's latent failure time model assumptions. It is assumed that lifetime distributions of latent causes of failure follow Weibull distribution with the same shape parameter, but different scale parameters. Maximum likelihood estimators (MLEs) of the unknown parameters can be obtained by solving a one-dimensional optimization problem, and we propose a fixed-point type algorithm to solve this optimization problem. Approximate MLEs have been proposed based on Taylor series expansion, and they have explicit expressions. Bayesian inference of the unknown parameters are obtained based on the assumption that the shape parameter has a log-concave prior density function, and for the given shape parameter, the scale parameters have Beta–Gamma priors. We propose to use Markov Chain Monte Carlo samples to compute Bayes estimates and also to construct highest posterior density credible intervals. Monte Carlo simulations are performed to investigate the performances of the different estimators, and two data sets have been analysed for illustrative purposes.     

论“立言”

两千多年前的春秋时代,中国知识分子就非常重视"立言",把它视作传名、追求不朽甚至永恒的重要手段。在建设文化强国的今天,继承"立言"的传统,把有价值的见解或史料、经验、发现等通过著书立说的方式贡献出来,是很有必要的。如何"立言",如何使自己所立之言得到社会的认可,并有较长的生命力,是目前知识界面临的难题。"立言"之人要有追求真理的精神、实事求是的态度;"立言"者须有创新意识,努力使自己的著作具有独创性;"立言"者还必须有精品意识,对自己的著作不断修改、加工,使之趋于完美;"立言"者须先修身,提高自身精神境界,更好地了解社会的需要和自己的责任。如此,方能"立言"成功。     

司法证明的维度之辨

准确认定案件事实是司法证明的核心目标.唯有基于准确的事实认定,当事人的权利和义务才能得到清晰界定.但"求真"过程本身存在致错风险,需要进行理性规制.与此同时,"求真"并非司法证明的全部目的.人的社会性赋予了共同体重要意义.司法证明还必须尊重和维护某些共同体的价值,即"求善".当前中国司法证明机制和实践过于强调追求案件真相,而忽视了"求善".总体而言,司法证明具有"求真"和"求善"两个维度,"求真"是为了维护个体权利,"求善"是为了维护和实现共同体的价值.唯有理清司法证明的双重维度,并在制度上对这两个维度及其竞合作出回应,才能促进司法与个人、社会之间的良性互动.     

模糊决策控制的动态经济调度方法

本文基于模糊数学的基本原理与负荷预报相结合,提出了一种计及辅助设备控制的动态经济调度方法。该方法利用模糊决策的理论对与辅助设备相对应的运行区域的启停和转换做出经济而可行的判断。把发电与负荷的平衡、费用消耗、区域运行时间及旋转备用看成相应的模糊子集,从而建立其相应隶属函数。通过算例的试算证明是可行的。     

毛泽东在延安整风运动中反对主观主义倡导实事求是的思想路线

在延安整风运动中,毛泽东运用了马列主义的世界观和方法论,从中国的实际出发,深刻地分析了党内主观主义及其危害,总结了中国革命遭受主观主义的统治而导致严重挫折的深刻教训,独创性地推行了一条马列主义原理与中国革命相结合,一切从实际出发,实事求是的思想路线,使中国共产党在错综复杂的环境中独立自主地找到了把中国革命引向胜利的道路。现在,这一思想路线仍然指导着中国的改革开放和现代化建设