Minimum variance unbiased estimation of stress–strength reliability under bivariate normal and its comparisons

In many industrial and natural phenomena, we need the probability that a component is smaller than the other component. Under a stress–strength model, this is reliability of an item. Under independent setup, there are different approaches for the estimation of such reliability. Here, estimation is considered under the dependent case. Under bi-variate setup uniformly minimum variance unbiased estimator is obtained. Also comparison with available estimator based on Maximum Likelihood Estimate (MLE) is done through Mean Square Error (MSE) and bias. Also these are compared by computing L₁ distance between their distribution functions. From this idea and numerical computations, UMVUE appears to be good.     

Reconciliation with the Utility of Chance by Elaborated Outcomes Destroys the Axiomatic Basis of Expected Utility Theory

Expected utility theory does not directly deal with the utility of chance. It has been suggested in the literature (Samuelson, 1952, Markowitz, 1959) that this can be remedied by an approach which explicitly models the emotional consequences which give rise to the utility of chance. We refer to this as the elaborated outcomes approach. It is argued that the elaborated outcomes approach destroys the possibility of deriving a representation theorem based on the usual axioms of expected utility theory. This is shown with the help of an example due to Markowitz. It turns out that the space of conceivable lotteries over elaborated outcomes is too narrow to permit the application of the axioms. Moreover it is shown that a representation theorem does not hold for the example.     

On the coase theorem and coalitional stability: the principle of equal relative concession

The Coase theorem is argued to be incompatible with bargaining set stability due to a tension between the grand coalition and sub-coalitions. We provide a counter-intuitive argument to demonstrate that the Coase theorem may be in complete consonance with bargaining set stability. We establish that an uncertainty concerning the formation of sub-coalitions will explain such compatibility: each agent fears that others may `gang up' against him and this fear forces the agents to negotiate. The grand coalition emerges from the negotiations if each agent uses the principle of equal relative sacrifice to determine the actual allocation. We also establish the rational basis for the choice of the principle of equal relative concession by the negotiating agents. Hence we argue that the Coase theorem will be valid even if there are stable sub-coalitions.     

会计盈余信息选拔的不可能定理及其理论深化

在美国等较为成熟的股票市场中,会计盈余信息的主要功能是定价,但是在政府管制较为严格的中国股票市场中,会计盈余信息的首要功能是"选拔".文章对中国证监会和上市公司之间的博弈构建了数学模型,提出了"会计盈余信息选拔的不可能定理":若以下两个条件存在--(1)监管部门设定选拔标准有一个上限,或(2)上市公司通过合法或非法方式虚报盈余的"虚报成本系数"较小,那么单纯依靠会计盈余信息将无法选拔出理想的目标公司.由此得到的可能的理论深化是:度量标准应当与契约形式相配合,如果制度环境本身限制了会计盈余信息作为度量标准的使用,那么改善的要点不应该集中于会计盈余信息本身,而应该在于调整博弈制度的安排.同时也为中国新会计准则执行研究提供了新的理论视角.     

Combinatorial Optimization in Real-Time Scheduling: Theory and Algorithms

Real-time computer systems are essential for many applications, such as robot control, avionics, medical instrumentation, manufacturing, etc. The correctness of the system depends on the temporal correctness as well as the functional correctness of the task executions. In order to assure temporal correctness it is necessary that the resources be scheduled to meet the temporal requirements of applications. When we consider the problem of nonpreemptive scheduling of a set of tasks in a processor for which no feasible solution exists, some tasks may have to be rejected so that a schedule can be generated for the rest. In this paper, we consider the problem of generating an optimal schedule such that the number of rejected tasks is minimized, and then the finish time is minimized for the accepted tasks. We propose to use an analytic approach to solve this problem. We first discuss the super sequence based technique which was originally proposed for reducing the search space in testing the feasibility of a task set. Then we show by the Conformation theorem that the super sequence constructed from the task set also provides a valid and reduced search space for the optimization problem. While the complexity of our scheduling algorithm in the worst case remains exponential, our simulation results show that the cost is reasonable for the average case.     

A quadratic lower bound for colourful simplicial depth

We show that any point in the convex hull of each of (d+1) sets of (d+1) points in ℝ ^d is contained in at least ⌊(d+2)²/4⌋ simplices with one vertex from each set. Both authors were supported by NSERC Discovery grants. Additionally, T. Stephen was supported by DFG FG-468 and the Dynamical Systems research focus at the University of Magdeburg.     

大学数学基础课教学中融入数学建模思想的实践

数学建模不仅限于解决实际问题,也可以是数学发展过程中提出的理论问题。基于近年来在大学数学基础课教学中融入数学建模思想的教学实践,论述了其主要思路与做法。介绍了将数学建模思想融入数学基础课教学的两个教学案例,即微积分方法的本质和从方程组出发引入线性相关与线性无关概念。     

On Bayesian D-optimum Design Criteria and the Equivalence Theorem in Non-linear Models

The concavity of some Bayesian D -optimality criteria is investigated and is found in some cases to depend on the prior distribution. In the case of a non-concave criterion, the standard equivalence theorem may fail, but a local version continues to apply.     

A simple approximation for the doubly noncentral t-distribution

A simple approximation for the doubly noncentral t-distribution, based upon the Fieller-Geary Theorem (1930) and approximate normality of the square root of the noncentral chi-square variable observed by Patnaik (1949), is developed, This approximation and an Edgeworth series expansion associated with it are evaluated. The simple approximation is seen to be reasonably accurate for most practical purposes.     

Inference for the Mean Residual Life Function via Empirical Likelihood

In addition to the distribution function, the mean residual life (MRL) function is the other important function which can be used to characterize a lifetime in survival analysis and reliability. For inference on the MRL function, some procedures have been proposed in the literature. However, the coverage accuracy of such procedures may be low when the sample size is small. In this article, an empirical likelihood (EL) inference procedure of MRL function is proposed and the limiting distribution of the EL ratio for MRL function is derived. Based on the result, we obtain confidence interval/band for the MRL function. The proposed method is compared with the normal approximation based method through simulation study in terms of coverage probability.