Generating autocorrelated pseudo-random numbers with specific distributions

An easily implemented and computationally efficient procedure is presented for the generation of autocorrelated pseudo-random numbers with specific probability distributions. A plot illustrates the relationship among the autocorrelations of the uniform, Rayleigh, and exponential distributions corresponding to a given autocorrelation in the normal generating distribution.     

The homotopy perturbation method for the Black–Scholes equation

The homotopy perturbation method is designed to obtain a quick and accurate solution to the Black–Scholes equation and boundary conditions for a European option pricing problem. The problem of pricing a European option can be cast a partial differential equation. The analytical solution of the equation is calculated in the form of a convergent power series with easily computable components.     

A note on estimating the common mean of k normal distributions and the stein problem

An unbiased estimator for the common mean of k normal distributions is suggested. A necessary and sufficient condition for the estimator Lo have a smaller variance than each sample mean is given. In the case of estimating the common mean vector of k p-variate (p ≤ 3) normal distributions a combined unbiased estimator may be used. We give a class of estimators which are better than the combined estimator when the loss is quadratic and the restriction of unbiasedness is removed.     

基于数理金融的保理业务探讨

本文应用数理金融法建立无追索保理业务定价模型,对保理业务参数对代偿概率的影响进行了敏感度分析。保理业务的定价不仅要考虑预期损失、成本、费用、收益等因素,还要把基础合同争议作为影响价格的因素。坏账担保率、应收账款的付款期限、应收账款池大小对代偿概率的影响比较明显。因此,为有效降低风险,建议保理商把坏账担保率设定在80%以下,付款期限设定在1年以内,并要求卖方转让全部应收账款。     

Circular balanced repeated measurements designs

The concept of a circular design is defined and when proper balance for various effects is assumed, its universal optimality is proved over the class of all designs with the same set of parameters, Such designs are shown to minimize the variance of the best linear unbiased estimators of contrasts of residual and direct effects over the class of equireplicated designs. All models assume first order residual effects and are of a circular nature. The proofs are presented in a unified manner for several models at a time. They are based on certain matrix domination which occurs when parameters are eliminated from a linear modelj this latter fact is proved for a general linear model.     

Estimation of the failure rate-a survey of nonparametric methods Part I: Non-Bayesian Methods

In this paper several nonparametric, non-Bayesian methods for estimating the failure rate function on which no monotonicity conditions have been imposed are surveyed. The survey attempts to consolidate and synthesize literature from several diverse areas of application, and endeavors to be as up-to-date as is feasible.     

喷涂工艺薄膜厚度模型的构建与应用

为研究12寸晶圆切割过程中喷涂工艺设备参数对保护性薄膜厚度的影响,提高设备调整效率和工艺质量,采用均匀设计的实验方法,以薄膜在测试量块上的厚度为目标,对影响厚度的主要因素:涂料压力、微调阀和雾化压力进行研究。对实验数据采用SPSS进行非线性逐步回归得到了薄膜厚度的数学模型,揭示了各因素的交互关系,为测机调整提供数据依据,节省大量反复测机时间,在保证工艺质量的同时提高了喷涂设备的生产效率。该模型已成功运用于某芯片封装测试厂的喷涂设备,并取得了显著效果。     

Exact tests for two-way symmetriccontingency tables

A two-way contingency table in which both variables have the same categories is termed a symmetric table. In many applications, because of the social processes involved, most of the observations lie on the main diagonal and the off-diagonal counts are small. For these tables, the model of independence is implausible and interest is then focussed on the off-diagonal cells and the models of quasi-independence and quasi-symmetry. For ordinal variables, a linear-by-linear association model can be used to model the interaction structure. For sparse tables, large-sample goodness-of-fit tests are often unreliable and one should use an exact test. In this paper, we review exact tests and the computing problems involved. We propose new recursive algorithms for exact goodness-of-fit tests of quasi-independence, quasi-symmetry, linear-by-linear association and some related models. We propose that all computations be carried out using symbolic computation and rational arithmetic in order to calculate the exact p-values accurately and describe how we implemented our proposals. Two examples are presented.     

False Discovery Rate Control of Step‐Up‐Down Tests with Special Emphasis on the Asymptotically Optimal Rejection Curve

Abstract. This paper is concerned with exact control of the false discovery rate (FDR) for step‐up‐down (SUD) tests related to the asymptotically optimal rejection curve (AORC). Since the system of equations and/or constraints for critical values and FDRs is numerically extremely sensitive, existence and computation of valid solutions is a challenging problem. We derive explicit formulas for upper bounds of the FDR and show that under a well‐known monotonicity condition, control of the FDR by a step‐up procedure results in control of the FDR by a corresponding SUD procedure. Various methods for adjusting the AORC to achieve finite FDR control are investigated. Moreover, we introduce alternative FDR bounding curves and study their connection to rejection curves as well as the existence of critical values for exact FDR control with respect to the underlying FDR bounding curve. Finally, we propose an iterative method for the computation of critical values.     

Designs balanced for circular residual effects

Magda (1980) introduced a model for repeated measurements designs with a circular structure of the residual effects. He proved the universal optimality of circular balanced uniform designs over a subclass of the possible designs. We strengthen his result to optimality over the set of all designs with the same number of experimental units, periods and treatments.