柯西积分概念与勒贝格积分概念的比较

介绍了柯西积分概念及定义在区间上的实函数的勒贝格积分概念 ,并将两者加以比较 .     

A simple approach to an integrated single-vendor single-buyer inventory system with shortage

In this article, a simple approach with two basic inequalities (Cauchy–Schwarz inequality and arithmetic–geometric mean inequality) is used to solve the integrated single-vendor single-buyer inventory problem developed by Wu and Ouyang (Wu, K.-S. and Ouyang, L.-Y., 2003. An integrated single-vendor single-buyer inventory system with shortage derived algebraically. Production Planning & Control, 14 (6), 555–561). Without the method of completing perfect square, the proposed approach yields the global minimum of the integrated total cost per year more easily than the algebraic approach used by Wu and Ouyang (2003 Wu, K-S and Ouyang, L-Y. 2003. An integrated single-vendor single-buyer inventory system with shortage derived algebraically. Production Planning & Control, 14(6): 555–561. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). In addition, for people without the background of calculus, it is more useful to determine the buyer's economic order quantity and the vendor's optimal number of deliveries.     

机械臂非线性定位方程计算新方法

针对机械臂定位算法中,数值算法计算量大,仿真过程存在累积误差,几何算法通用性不强等问题,以手术机器 人六自由度机械臂为研究对象,建立了一组多关节机械臂非线性定位方程组,提出了其基于非线性大范围渐近稳定的 求解方法。结果表明该方法既简化运算,又有利于物理实现,为机械臂高速、准确运动提供了基础,实验表明该算法适用 多关节的移动机械臂的非线性定位方程的求解,有较高的求解精度和收敛速度。     

On the distribution of products of independent beta variates

This paper concerns an inquiry into the problem of generating closed form expressions for the cumulative distribution and probability density functions of products of independent beta variates. Recursive analytical procedures for constructing the equational forms of these functions-from their Mellin inversion integral representations, via the Cauchy residue theorem-are described. A numerical example illustrating details of the construction of a computable form of the distribution function of the product of three independent beta variates is also included.     

State space modeling of multiple time series: a comment

This paper provides guidance in choosing k₁ andk₂ of the double k-class (KK) estimator such that it will improve upon both the ordinary least squares (OLS) and Stein-rule (SR) estimators in predictive mean squared error (PMSE). Asymptotic bias and mean squared error (MSE) results are derived for nonnormal and other cases. A simulation compares the KK estimator with the OLS and SR estimators.     

Sample Size and Power Calculations for Left-Truncated Normal Distribution

Abstract

Sample size calculation is an important component in designing an experiment or a survey. In a wide variety of fields—including management science, insurance, and biological and medical science—truncated normal distributions are encountered in many applications. However, the sample size required for the left-truncated normal distribution has not been investigated, because the distribution of the sample mean from the left-truncated normal distribution is complex and difficult to obtain. This paper compares an ad hoc approach to two newly proposed methods based on the Central Limit Theorem and on a high degree saddlepoint approximation for calculating the required sample size with the prespecified power. As shown by use of simulations and an example of health insurance cost in China, the ad hoc approach underestimates the sample size required to achieve prespecified power. The method based on the high degree saddlepoint approximation provides valid sample size and power calculations, and it performs better than the Central Limit Theorem. When the sample size is not too small, the Central Limit Theorem also provides a valid, but relatively simple tool to approximate that sample size.     

On a Generalization of Bivariate Cauchy Distribution

This paper addresses a generalization of the bivariate Cauchy distribution discussed by Fang et al. (1990 Fang , K. T. , Kotz , S. , Ng , K. W. ( 1990 ). Symmetric Multivariate and Related Distributions . London : Chapman and Hall .[Crossref] , [Google Scholar]), derived from a trivariate normal distribution with a general correlation matrix. We obtain explicit expressions for the joint distribution function and joint density function, and show that they reduce in a special case to the corresponding expressions of Fang et al. (1990 Fang , K. T. , Kotz , S. , Ng , K. W. ( 1990 ). Symmetric Multivariate and Related Distributions . London : Chapman and Hall .[Crossref] , [Google Scholar]). Finally, we show that this generalized distribution is useful in determining the orthant probability of a bivariate skew-normal distribution of Azzalini and Dalla Valle (1996 Azzalini , A. , Dalla Valle , A. ( 1996 ). The multivariate skew-normal distribution . Biometrika 83 : 715 – 726 .[Crossref], [Web of Science ®] , [Google Scholar]).     

New Generalizations of Cauchy Distribution

The generalized skew-normal distribution introduced by Balakrishnan (2002 Balakrishnan , N. ( 2002 ). Discussion on ‘Skew multivariate models related to hidden truncation and/or selective reporting’ by B. C. Arnold and R. J. Beaver . Test 11 : 37 – 39 .[Web of Science ®] , [Google Scholar]) is used to obtain new generalizations of univariate Cauchy distribution with two parameters, denoted by GC _{m, n} (a, b) with m and n non-negative integer numbers and a, b ∈ R. For cases (m, n) = (1, 2), (m, n) = (2, 1), (m, n) = (0, 3) and (m, n) = (3, 0) explicit forms of the density functions are derived and compared to previous generalizations of Cauchy and skew-Cauchy distributions.     

Some bivariate uniform distributions

Bivariate uniform distributions with dependent components are readily derived by distribution function transformations of the components of non-uniform dependent continuous bivariate random variables (X,Y). Contour plots of joint density functions show the various, and varying, forms of dependence which can arise from different distributional forms for (X,Y) and aids the choice of bivariate uniform distributions as empirical models.     

Test of symmetry based on copula function

We introduce some new nonparametric statistical tests of symmetry. The limiting behaviors of the proposed statistics are established under the null hypothesis. Emphasis is placed on explanation of the strong approximation methodology. The asymptotic validity of a re-sampling method to compute p-values is also established. A simulation study for some considered statistics is performed.