Testing Extreme Value Conditions

A test statistic is developed that checks the validity of the extreme value conditions without specifiying the shape parameter of the limiting extreme value distribution.     

Gas chromatography of halogenated adamantanes

The main thermodynamic characteristics of the adsorption of haloadamantanes on graphitized thermal carbon black were determined by experimental measurements and by calculations in terms of molecular-statistic theory of adsorption. Using experimental data, the Kovac retention indices were calculated and the optimum conditions for gas-chromatographic separation of haloadamantanes on stationary phases with different polarity were elucidated. The influence of the cage effect in the adamantane unit on the chromatographic properties of haloadamantanes was established.     

Asymptotic expansions of the distributions of some test statistics

Summary A modified Wald statistic for testing simple hypothesis against fixed as well as local alternatives is proposed. The asymptotic expansions of the distributions of the proposed statistic as well as the Wald and Rao statistics under both the null and alternative hypotheses are obtained. The powers of these statistics are compared and its is shown that for special structures of parameters some statistics have same power in the sence of order . The results obtained are applied for testing the hypothesis about the covariance matrix of the multivariate normal distribution and it is shown that none of the tests based on the above statistics is uniformly superior. Research supported by the National Science Foundation Grant MCS 830149.     

Closer asymptotic approximations for the distributions of the power divergence goodness-of-fit statistics

Summary The members of the power divergence family of statistics all have an asymptotically equivalent χ² distribution (Cressie and Read [1]). An asymptotic expansion for the distribution function is derived which shows that the speed of convergence to this asymptotic limit is dependent on λ. Known results for Pearson'sX ² statistic and the log-likelihood ratio statistic then appear as special cases in a continuum rather than as separate (unrelated) expansions.     

SOLVERSTAT: a new utility for multipurpose analysis. An application to the investigation of dioxygenated Co(II) complex formation in dimethylsulfoxide solution

A new utility for multipurpose analysis, SOLVERSTAT, taking advantage of the versatility of spreadsheets is here described. By means of this tool advanced statistical tests have introduced in Microsoft Excel Solver thus allowing regression diagnostic and discrimination between different models. The utility is here applied to the determination, by UV-Vis spectroscopy, of the stability constant for the uptake of molecular dioxygen by the 1:2 complex of Co(II) with N,N′-dimethylethylenediamine (dmen) in the aprotic solvent dimethylsulfoxide (dmso) at 298 K and in a medium adjusted to 0.1 mol dm⁻³ with Et₄NClO₄. The reliability of the model and parameters obtained are discussed and the results compared with those obtained by Dynafit, a different software package, and by independent voltammetric measurements. The validity of SOLVERSTAT has been also examined applying it to the discrimination between different models already discussed in the literature.     

Importance Sampling for p-value Computations in Multivariate Tests

Abstract

An importance sampling procedure is developed to approximate the distribution of an arbitrary function of the eigenvalues for a matrix beta random matrix or a Wishart random matrix. The procedure is easily implemented and provides confidence intervals for the p-values of many of the commonly used test statistics in multivariate analysis. An adaptive procedure allows for the control of either absolute error or relative error in this p-value estimation through the choice of importance sample size.     

Surface Tension of Ternary Liquid Mixtures

Abstract

Surface tension has been measured by the differential capillary rise method for three ternary mixtures containing alkanes (hexane + cyclohexane+benzene, pentane + hexane + benzene and cyclohexane + heptane + toluene at 298.15\pm 0.1°K). The sign and magnitude of the excess surface tension and excess volume depend ultimately upon the chain length of the component of the mixtures. The results of the surface tension were compared with theoretical values obtained from Flory theory, Sanchez method, Brock-Bird relation and volume fraction statistics. There is reasonable agreement between theory and experiment.     

One physical problem with possible mathematical significance

We analyze three-dimensional gauge theory with Chern-Simons action, which arises in the context of high T_c superconductivity. We show that the main effect in this theory is the change of spin and statistics of charged particles. Also, the amplitudes of particle propagation acquire phases dependent on the topology of the knot formed by their trajectories. In the end, we discuss possible generalizations of this theory, and their relations to strings.     

主成分分析应用方法的改进

首先对主成分分析应用中出现的一些误区,通过推导指出错误所在,并提出相应的改进方案.最后通过一个实例,说明新方案的合理性.     

高血压性脑出血再发生因素的Logistic分析

根据问题的特点 ,选择 Logistic判别模型 ,并借鉴普通线性回归的逐步向前法 ,用似然比统计量 ( Deviance)来筛选自变量 (因素 ) .结果显示 :在 1 1个因素中 ,有 3个是作用显著的 ,而其中舒张压值极为重要 .为降低再出血率 ,将其控制在 85 mm Hg以下是有效而可行的