Estimation in Maxwell distribution with randomly censored data

In many practical situations, complete data are not available in lifetime studies. Many of the available observations are right censored giving survival information up to a noted time and not the exact failure times. This constitutes randomly censored data. In this paper, we consider Maxwell distribution as a survival time model. The censoring time is also assumed to follow a Maxwell distribution with a different parameter. Maximum likelihood estimators and confidence intervals for the parameters are derived with randomly censored data. Bayes estimators are also developed with inverted gamma priors and generalized entropy loss function. A Monte Carlo simulation study is performed to compare the developed estimation procedures. A real data example is given at the end of the study.     

热力学基本方程、对应系数关系式和麦克斯韦关系式的简捷记忆

热力学关系式多而杂,学生记忆十分困难。提出了热力学基本方程、对应系数关系式和麦克斯韦关系式的一种简捷记忆方法,不仅使学生能容易记住各种关系式,而且提高了记忆的准确度和牢固度。     

图形记忆法-几个热力学关系的记忆规律探讨

利用一种图形,将特性函数、四个特性函数之间的关系、特性函数的微分表示、麦氏关系、四个态变量的偏导表示、系统总特性函数存在条件、几个常用的热力学系数的定义公式等记忆方法纳入其中,用简单易记的形式使在系统的热力学性质推演中常用的繁杂的公式记忆简化,提高了记忆的准确度和牢固度。     

Tests of marginal homogeneity and special cases

The analysis of two‐way contingency tables is common in clinical studies. In addition to summary counts and percentages, statistical tests or summary measures are often desired. If the data can be viewed as two categorical measurements on the same experimental unit (matched pair data) then a test of marginal homogeneity may be appropriate. The most common clinical example is the so called ‘shift table’ whereby a quantity is tested for change between two time points. The two principal marginal homogeneity tests are the Stuart Maxwell and Bhapkar tests. At present, SAS software does not compute either test directly (for tables with more than two categories) and a programmatic solution is required. Two examples of programmatic SAS code are found in the current literature. Although accurate in most instances, they fail to produce output for certain tables (‘special cases’). After summarizing the mathematics behind the two tests, a SAS macro is presented, which produces correct output for all tables. Finally, several examples are coded and presented with resultant output. Copyright © 2013 John Wiley & Sons, Ltd.     

麦克斯韦方程的爱因斯坦符号表示

本文介绍了爱因斯坦符号在麦克斯韦理论中的应用,着重讨论了麦克斯韦方程的微分形式和积分形式的等价问题。     

Higher order expansion for moments of extreme for generalized Maxwell distribution

In this paper, the higher order asymptotic expansion of the moments of extreme from generalized Maxwell distribution is gained, by which one establishes the rate of convergence of the moment of the normalized partial maximum to the moment of the associated Gumbel extreme value distribution.     

COM–Poisson cure rate survival models and an application to a cutaneous melanoma data

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow the Conway–Maxwell Poisson distribution. This model includes as special cases some of the well-known cure rate models discussed in the literature. Next, we discuss the maximum likelihood estimation of the parameters of this cure rate survival model. Finally, we illustrate the usefulness of this model by applying it to a real cutaneous melanoma data.     

电磁场教学中电场的计算

电磁场的求解问题，主要归结为求电场和磁场的问题，其中关于电场的求解主要是求电场强度。不同电场，电场强度的计算方法也不同。以所学电磁场知识为基础，从静态场与动态场两种角度，归纳出几种求解电场强度的方法，并分别给出这些方法的适用范围。     

Uncertainty estimation in heterogeneous capture–recapture count data

The Conway–Maxwell–Poisson estimator is considered in this paper as the population size estimator. The benefit of using the Conway–Maxwell–Poisson distribution is that it includes the Bernoulli, the Geometric and the Poisson distributions as special cases and, furthermore, allows for heterogeneity. Little emphasis is often placed on the variability associated with the population size estimate. This paper provides a deep and extensive comparison of bootstrap methods in the capture–recapture setting. It deals with the classical bootstrap approach using the true population size, the true bootstrap, and the classical bootstrap using the observed sample size, the reduced bootstrap. Furthermore, the imputed bootstrap, as well as approximating forms in terms of standard errors and confidence intervals for the population size, under the Conway–Maxwell–Poisson distribution, have been investigated and discussed. These methods are illustrated in a simulation study and in benchmark real data examples.     

麦克斯韦与物理学的发展

本文主要从电磁场理论和气动理论两个方面阐述了麦克斯韦对物理学发展所做出的巨大贡献。