凸轮磨削数控程序的设计

本文叙述了几种由不同数学函数描述的凸轮型面的数控磨削方法。它们可以是外型面,也可以是内型面的。对于因砂轮直径偏差(刀具)或者被磨削型面基圆偏差(工件)所引起的加工误差也作了分析。最后提出一种采用对分试算法计算刀具轨迹的新方法,可简化数控编程计算问题。     

一种用于随机共振数值模拟的二阶方法

本文推导了一种可用于不同种类噪声产生的随机共振数值模拟的二阶积分方法,它也可用于相干共振的数值模拟,该方法具有精度较好、效率较高的优点.     

Comparing several exponential populations with more than one control

Suppose there are k ₁ (k ₁ ≥ 1) test treatments that we wish to compare with k ₂ (k ₂ ≥ 1) control treatments. Assume that the observations from the ith test treatment and the jth control treatment follow a two-parameter exponential distribution and , where θ is a common scale parameter and and are the location parameters of the ith test and the jth control treatment, respectively, i = 1, . . . ,k ₁; j = 1, . . . ,k ₂. In this paper, simultaneous one-sided and two-sided confidence intervals are proposed for all k ₁ k ₂ differences between the test treatment location and control treatment location parameters, namely , and the required critical points are provided. Discussions of multiple comparisons of all test treatments with the best control treatment and an optimal sample size allocation are given. Finally, it is shown that the critical points obtained can be used to construct simultaneous confidence intervals for Pareto distribution location parameters.     

Asymptotic Distribution of the Maximum Likelihood Estimators of the Parameters of the Right-Truncated Dagum Distribution

In this work we have determined the asymptotic distribution of the maximum likelihood estimators of the parameters β, λ, and δ for the right-truncated Dagum model. Some numerical comparisons show that, for each combination of the parameters and for each sample size, the variance of maximum likelihood estimators increases as the truncation point decreases, i.e., with the increase in the cut of the right tail of distribution.     

Composite Likelihood Estimation for Multivariate Probit Latent Traits Models

Inference in generalized linear mixed models with multivariate random effects is often made cumbersome by the high-dimensional intractable integrals involved in the marginal likelihood. This article presents an inferential methodology based on the marginal composite likelihood approach for the probit latent traits models. This method belonging to the broad class of pseudo-likelihood involves marginal pairs probabilities of the responses which has analytical expression. The different results are illustrated with a simulation study and with an analysis of real data from health related quality of life.     

IMPROVING THE NUMERICAL TECHNIQUE FOR COMPUTING THE ACCUMULATED DISTRIBUTION OF A QUADRATIC FORM IN NORMAL VARIABLES

ABSTRACT

This paper is concerned with the technique of numerically evaluating the cumulative distribution function of a quadratic form in normal variables. The efficiency of two new truncation bounds and all existing truncation bounds are investigated. We also find that the suggestion in the literature for further splitting truncation errors might reduce computational efficiency, and the optimum splitting rate could be different in different situations. A practical solution is provided. The paper also discusses a modified secant algorithm for finding the critical value of the distribution at any given significance level.     

PIECEWISE POLYNOMIAL APPROXIMATIONS FOR HEAVY-TAILED DISTRIBUTIONS IN QUEUEING ANALYSIS

ABSTRACT

A basic difficulty in dealing with heavy-tailed distributions is that they may not have explicit Laplace transforms. This makes numerical methods that use the Laplace transform more challenging. This paper generalizes an existing method for approximating heavy-tailed distributions, for use in queueing analysis. The generalization involves fitting Chebyshev polynomials to a probability density function g(t) at specified points t ₁, t ₂, …, t _N . By choosing points t _i , which rapidly get far out in the tail, it is possible to capture the tail behavior with relatively few points, and to control the relative error in the approximation. We give numerical examples to evaluate the performance of the method in simple queueing problems.     

Analysis of over-dispersed count data with extra zeros using the Poisson log-skew-normal distribution

ABSTRACT

Mixed Poisson distributions are widely used in various applications of count data mainly when extra variation is present. This paper introduces an extension in terms of a mixed strategy to jointly deal with extra-Poisson variation and zero-inflated counts. In particular, we propose the Poisson log-skew-normal distribution which utilizes the log-skew-normal as a mixing prior and present its main properties. This is directly done through additional hierarchy level to the lognormal prior and includes the Poisson lognormal distribution as its special case. Two numerical methods are developed for the evaluation of associated likelihoods based on the Gauss–Hermite quadrature and the Lambert's W function. By conducting simulation studies, we show that the proposed distribution performs better than several commonly used distributions that allow for over-dispersion or zero inflation. The usefulness of the proposed distribution in empirical work is highlighted by the analysis of a real data set taken from health economics contexts.     

Pooling multivariate data

In case it is doubtful whether two sets of data have the same mean vector, four estimation strategies have been developed for the target mean vector. In this situation, the estimates based on a preliminary test as well as on Stein-rule are advantageous. Two measures of relative efficiency are considered; one based on thequadratic loss function, and the other on the determinant of the mean square error matrix. A max-min rule for the size of the preliminary test of significance is presented. It is demonstrated that the shrinkage estimator dominates the classical estimator, whereas none of the shrinkage estimator and the preliminary test estimator dominate each other. The range in the parameter space where preliminary test estimator dominates shrinkage is investigated analytically and computationally. It is found that the shrinkage estimator outperform the preliminary test estimator except in a region around the null hypothesis. Moreover, for large values of a, the level of statistical significance, shrinkage estimator dominates the preliminary test estimator uniformly. The relative dominance of the estimators is presented.