粗糙磨损表面特征的双谱分析

采用双谱分析技术，结合表面粗糙度偏斜度评定参数的定义，给出了偏斜度函数的双谱表达式；在对工程粗糙表面的偏斜度进行理论研究的基础上，分析了精密车削和磨削加工试件磨损前后表面高度分布的偏斜度．结果表明，可以用双谱和偏斜度函数对粗糙磨损表面非对称高度分布进行直观和便捷的评价．     

基于Beta分布形状的拟合优度检验

本文指出了拟合优度检验中选用经验频率公式时存在的误区,对顺序统计量失效概率分布进行了偏态和峰态分析,提出了一个基于Beta分布形状特征的经验分布函数,给出了精确值和近似值两种计算方法,在此基础上建立新的极值型检验统计量．利用Monte Carlo方法进行数值模拟,得到0．01、0．05、0．1显著度水平下检验统计量的临界值,并利用常用的分布模型进行检验功效比较,数值模拟结果表明基于分布形状的经验频率公式能更好地反映顺序统计量失效概率分布的集中趋势,证明了本文提出的两种检验统计量在中小样本条件下具有更优的检验功效．     

The information matrix,skewness tensor and a-connections for the general multivariate elliptic distribution

Expressions for the entries of the information matrix and skewness tensor of a general multivariate elliptic distribution are obtained. From these the coefficients of the a-connections are derived. A general expression for the asymptotic efficiency of the sample mean, when appropriate as an estimator of the location parameter, is obtained. The results are illustrated by examples from the multivariate normal, Cauchy and Student's t-distributions.     

Study of the Second-Order Nonlinear Characteristics of Ocean Waves (Ⅰ)——Theoretical Derivation

This paper investigates the second-order nonlinear characteristics of random waves. Based upon the solutions derived strictly for 3-dimensional random waves in water of arbitrary uniform depth , the sea surface skewness and the second-order spectrum are exactly rededuced in a more reasonable way, and the bispectrum of sea surface elevation is theoretically given for the first time.     

Likelihood ratio tests for symmetry against one-sided alternatives

A random variableX is said to have a symmetric distribution (about 0) if and only ifX and –X are, identically distributed. By considering various types of partial orderings between the distributions ofX and –X, one obtains various notions of skewness or one-sided bias. In this paper we study likelihood ratio tests for testing the symmetry of a discrete distribution about zero against the alternatives, (i)X is stochastically greater than –X; and (ii) pr(X=j)pr(X=–j) for allj>0. In the process, we obtain maximum likelihood estimators of the distribution function under the above alternatives. The asymptotic null distributions of the test statistics have been obtained and are of the chi-bar square type. A simulation study was performed to compare the powers of these tests with other tests.     

Gradient skewness tensors and local illumination detection for images

In this paper, we propose the definition of D$D$-eigenvalue for an arbitrary order tensor related with a second-order tensor D$D$, and introduce the gradient skewness tensor which involves a three-order tensor derived from the skewness statistic of gradient images. As we happen to find out that the skewness of oriented gradients can measure the directional characteristic of illumination in an image, the local illumination detection problem for an image can be abstracted as solving the largest D$D$-eigenvalue of gradient skewness tensors. We discuss the properties of D$D$-eigenvalues, and especially for gradient skewness tensors we provide the calculation method of its D$D$-eigenvalues and D$D$-characteristic polynomial. Some numerical experiments show its effective application in illumination detection. Our method also presents excellent results in a class of image authenticity verification problems, which is to distinguish artificial “flat” objects in a photograph.     

On the existence of multiply connected monolayered cyclofusenes with given parameters

For a given bipartite graph G its skewness is defined as the difference between the sizes of its classes of bipartition. We show that a multiply connected monolayered cyclofusene with m ≥ 2 internal holes and skewness k exists if and only if 0 ≤ k ≤ 2m − 2, thus settling in affirmative two conjectures raised in a recent paper by Karimi et al.