Order Statistics from the Generalized Exponential Distribution and Applications

With linear dispersion effects, the standard factorial designs are not optimal estimation of a mean model. A sequential two-stage experimental design procedure has been proposed that first estimates the variance structure, and then uses the variance estimates and the variance optimality criterion to develop a second stage design that efficiency estimates the mean model. This procedure has been compared to an equal replicate design analyzed by ordinary least squares, and found to be a superior procedure in many situations.

However with small first stage sample sizes the variance estiamtes are not reliable, and hence an alternative procedure could be more beneficial. For this reason a Bayesian modification to the two-stage procedure is proposed which will combine the first stage variance estiamtes with some prior variance information that will produce a more efficient procedure. This Bayesian procedure will be compared to the non-Bayesian twostage procedure and to the two one-stage alternative procedures listed above. Finally, a recommendation will be made as to which procedure is preferred in certain situations.     

Interpreting the Principal Component Analysis of Multivariate Density Functions

Functional principal component analysis (FPCA) as a reduction data technique of a finite number T of functions can be used to identify the dominant modes of variation of numeric three-way data.

We carry out the FPCA on multidimensional probability density functions, relate this method to other standard methods and define its centered or standardized versions. Grounded on the relationship between FPCA of densities, FPCA of their corresponding characteristic functions, PCA of the MacLaurin expansions of these characteristic functions and dual STATIS method applied to their variance matrices, we propose a method for interpreting the results of the FPCA of densities. This method is based on the investigations of the relationships between the scores of the FPCA and the moments associated to the densities.

The method is illustrated using known Gaussian densities. In practice, FPCA of densities deals with observations of multidimensional variables on T occasions. These observations can be used to estimate the T associated densities (i) by estimating the parameters of these densities, assuming that they are Gaussian, or (ii) by using the Gaussian kernel method and choosing the matrix bandwidth by the normal reference rule. Thereafter, FPCA estimate is derived from these estimates and the interpretation method is carried out to explore the dominant modes of variation of the types of three-way data encountered in sensory analysis and archaeology.     

The construction of optimal histograms

In this note, a stopping rule is derived that gives the optimal histogram bin width to approximate a probability density function, The procedure minimizes the mean integrated square error between the density function and the histogram, and requires no prior knowledge of the density function.     

数字易卦与易经

数字易卦的源头可上溯到八千年前。自伏羲时代经炎黄时代到夏商时代,数字易卦走过了它五千余载的漫长历程。出土的大量文物考古资料表明:数字易卦本为易经的根基和来源,易经则为数字易卦的演变、发展、升华和突变;二者之间是源和流的关系,是从渐变到突变的发展,是由量变到质变的必然。     

A procedure for approximate negative binomial tolerance intervals

In this article, we present a procedure for approximate negative binomial tolerance intervals. We utilize an approach that has been well-studied to approximate tolerance intervals for the binomial and Poisson settings, which is based on the confidence interval for the parameter in the respective distribution. A simulation study is performed to assess the coverage probabilities and expected widths of the tolerance intervals. The simulation study also compares eight different confidence interval approaches for the negative binomial proportions. We recommend using those in practice that perform the best based on our simulation results. The method is also illustrated using two real data examples.     

化学教学中的发散思维及其培养

理论联系实际地阐述了发散思维的原理与方法,说明了在化学教学中培养学生的发散思维对于增强学生能力、提高学生素质的重要意义。     

399种高校学报开本及幅面尺寸调查

对2008年出版的399种公开发行的高校学报的开本及幅面尺寸进行调查.对高校学报开本及幅面尺寸存在的问题和开本及幅面尺寸不符合国家标准的原因进行了分析,并提出了实现标准化的建议.     

从“音律正变”理论到格调说——《唐音》在元明诗学嬗变中的理论意义

明代诗学以格调说为中心,对中国诗歌的美学结构和风格进行了深入的探讨,成就是巨大的。为理清格调说的理论内含,必须对其理论来源进行研究。本文对明代前期——格调说的形成期理论的衍变进行了分析,汰去旧说对《唐诗品汇》的误解,着重论述《唐音》的音律正变理论对于格调说的导引意义。     

Could hemogram parameters be predictors of dementia in elderly patients?

Objective: To study red cell distribution width (RDW), RDW to platelet ratio (RPR) and mean platelet volume to platelet ratio (MPR), novel inflammatory markers of routine hemogram, of patients with or without dementia, according to the grade of the disease established by Fazekas’s score in magnetic resonance imaging (MRI).

Methods: A total of 1342 cases that undergone cranial MRI study were retrospectively analyzed. Patients without a previous stroke and over 45 years were enrolled in the study. Demographic and laboratory characteristics of the participants were obtained from institutional computerized database. Subcortical and periventricular white matter were evaluated in axial FLAIR images according to Fazekas’s grading scale. Univariate and multivariate analysis were performed for assessing the predictors of Fazekas’s grading scale.

Results: MPR of Fazekas 0, Fazekas 1, Fazekas 2 and Fazekas 3 groups were 3, 3, 4 and 3%, respectively. MPR difference between study groups was not significant (p?=?.32). RPR of Fazekas 0, Fazekas 1, Fazekas 2 and Fazekas 3 groups were 6, 7, 7 and 7%, respectively. RPR difference between study groups was significant (p?Conclusion: We suggest that increased RDW and RPR values may indicate higher Fazekas’s score and dementia in cranial imaging studies. The radiologist should pay particular attention in interpretation of cranial MRI of these patients.     

On the use of general positive quadratic forms in simultaneous inference

Some aspects of using general positive definite quadratic forms to project simultaneous confidence intervals for scalar linear functions of a parameter vector are explored. Firstly, a criterion is introduced according to which Scheffe’s S-method (using the inverse of the dispersion matrix of the allied estimators) is optimal. Secondly, it is shown how to construct simultaneous confidence bands (for regression surfaces) with minimal confidence interval length at a given arbitrary point.