Harmonic mean approach to uunbalanced random effects models under heteroscedasticity

In this paper we consider unbalanced random effects models under heteroscedastic variances. By using' the harmonic mean approach, it is shown that the problems are analogous to those from balanced random effects models under horaoscedastic variances. Thus, by using the harmonic mean approach, statistical inferences about variance components are derived by using procedures from balanced models under homoscedastic variances. Laguerre polynomial expansion is used to approximate the sampling distributions of relevant statistics.     

Stationary analysis of a BMAP/R/1 queue with R-type multiple working vacations

We consider an infinite-buffer single server queue with batch Markovian arrival process (BMAP) and exhaustive service discipline under multiple working vacation policy. The service time during a working vacation is generally distributed random variable which is independent of the service times during a normal busy period as well as the arrival process. Duration of service times during a normal busy period and duration of working vacation times follow the class of distributions whose Laplace-Stieltjes transforms are rational functions (R-type distributions). The service time during a normal busy period, working vacation time, and the service time during a working vacation are independent of each other as well as of the arrival process. If a working vacation terminates while service is going on for a customer at head of the queue in vacation mode then, the server switches to normal mode and the customer at head of the queue is entitled to receive a full service time in the normal busy period irrespective of the amount of service received by the customer at head of the queue during the previous working vacation period. We obtain system-length distributions at various epoch, such as post-departure, pre-arrival, arbitrary, and pre-service. The proposed analysis is based on the use of matrix-analytic procedure to obtain system-length distribution at post-departure epoch. Later, we use supplementary variable technique and simple algebraic manipulations to obtain system-length distribution at arbitrary epoch using the system-length distribution at post-departure epoch. Some important performance measures, such as mean system lengths and mean waiting time have been obtained. Finally, some numerical results have been presented in the form of tables and graphs to show the applicability of the results obtained in this article. The model has potential application in areas of computer and communication networks, such as ethernet passive optical network (EPON).     

On the rate of convergence of the Robbins–Monro's algorithm in a linear stochastic ill-posed problem with α-mixing data

In this paper we consider a recursive method of Robbins–Monro type to estimate the solution of the linear problem Ax = u, in which the second member is measured with α-mixing errors. We also show the almost complete convergence (a.co) of this algorithm specifying its convergence rate.     

Fractional Age Assumption Based on Cubic Polynomial Interpolation

This article proposes a new fractional age assumption (FAA) based on the cubic polynomial interpolation (CPI) and applies it to estimate the mortality rate and related actuarial quantities. The validity of the method under CPI is proved theoretically and the valuable advantages of CPI assumption are discussed based on three different perspectives—utilized death information, property of mortality force, and optimality criterion. The results show that CPI assumption has distinct valuable superiority compared with other FAAs in references. Finally under CPI assumption we study the calculations of some important actuarial quantities in life contingencies.     

A variant of K nearest neighbor quantile regression

Compared with local polynomial quantile regression, K nearest neighbor quantile regression (KNNQR) has many advantages, such as not assuming smoothness of functions. The paper summarizes the research of KNNQR and has carried out further research on the selection of k, algorithm and Monte Carlo simulations. Additionally, simulated functions are Blocks, Bumps, HeaviSine and Doppler, which stand for jumping, volatility, mutagenicity slope and high frequency function. When function to be estimated has some jump points or catastrophe points, KNNQR is superior to local linear quantile regression in the sense of the mean squared error and mean absolute error criteria. To be mentioned, even high frequency, the superiority of KNNQR could be observed. A real data is analyzed as an illustration.     

序信息系统与粗糙集介绍及研究综述

本文介绍序信息系统中粗糙集理论的基本概念,通过分析和回顾序信息系统粗糙集的方法和研究现状,给出了该领域下一步的研究重点和主要方向,为充实和完善序信息系统粗糙集理论与方法奠定了基础.     

Securing Children’s Best Interests While Resisting the Lure of Simple Solutions

The best-interest-of-the-child standard for child custody policy and decisions has benefits and hazards, the latter related to the exercise of judicial discretion in custody disputes. This article examines alternatives to the status quo, including the primary parent presumption, the approximation rule, shared parenting, an exact even split of custodial time, sole custody for couples labeled as in high conflict or those with young children, the friendly parent presumption, and decisions that defer to children’s stated preferences. Each alternative promises simpler paths to securing children’s welfare, but some have more support than others in the social science literature.     

关于多元Ismail-May算子的一致逼近

主要讨论了多元Ismail—May算子的一致逼近问题，利用多元分解技巧和已有的一元结论给出了多元Ismail—May算子逼近阶的估计和特征刻划．     

Optimal testing and repairing a failed series system

We consider a series repairable system that includes n components and assume that it has just failed because exactly one of its components has failed. The failed component is unknown. Probability of each component to be responsible for the failure is given. Each component can be tested and repaired at given costs. Both testing and repairing operations are assumed to be perfect, that is, the result of testing a component is a true information that this component is failed or active (not failed), and the result of repairing is that the component becomes active. The problem is to find a sequence of testing and repairing operations over the components such that the system is always repaired and the total expected cost of testing and repairing the components is minimized. We show that this problem is equivalent to minimizing a quadratic pseudo-boolean function. Polynomially solvable special cases of the latter problem are identified and a fully polynomial time approximation scheme (FPTAS) is derived for the general case. Computer experiments are provided to demonstrate high efficiency of the proposed FPTAS. In particular, it is able to find a solution with relative error ɛ = 0.1 for problems with more than 4000 components within 5 minutes on a standard PC with 1.2 Mhz processor.     

一类正交多项式的两种并行算法

通过修正计算Chebyshev多项式的Forsythe算法和Clenshaw算法 ,提出了求解一类正交多项式的两种并行算法 ,并对其稳定性进行了分析 .