Efficient Estimation of a Distribution Function under Quadrant Dependence

LetX₁,X₂, ..., be real-valued random variables forming a strictly stationary sequence, and satisfying the basic requirement of being either pairwise positively quadrant dependent or pairwise negatively quadrant dependent. LetF^ be the marginal distribution function of theX_ips, which is estimated by the empirical distribution functionF_n and also by a smooth kernel-type estimateF_n, by means of the segmentX₁, ...,X_n. These estimates are compared on the basis of their mean squared errors (MSE). The main results of this paper are the following. Under certain regularity conditions, the optimal bandwidth (in the MSE sense) is determined, and is found to be the same as that in the independent identically distributed case. It is also shown thatn MSE(F_n(t)) andnMSE (F^_n(t)) tend to the same constant, asn→∞ so that one can not discriminate be tween the two estimates on the basis of the MSE. Next, ifi(n) = min {k∈{1, 2, ...}; MSE (F_k(t)) ≤ MSE (F_n(t))}, then it is proved thati(n)/n tends to 1, asn→∞. Thus, once again, one can not choose one estimate over the other in terms of their asymptotic relative efficiency. If, however, the squared bias ofF^_n(t) tends to 0 sufficiently fast, or equivalently, the bandwidthh_n satisfies the requirement thatnh³_n→ 0, asn→∞, it is shown that, for a suitable choice of the kernel, (i(n) ?n)/(nh_n) tends to a positive number, asn→∞ It follows that the deficiency ofF_n(t) with respect toF^_n(t),i(n) ?n, is substantial, and, actually, tends to ∞, asn→∞. In terms of deficiency, the smooth estimateF^_n(t) is preferable to the empirical distribution functionF_n(t)     

体词谓语句的生成条件

体词谓语句是以体词作谓语,能够自由生存的句子,它是现代汉语中一种独立的句型而非动词句的省略。体词具备陈述功能,是其作谓语的语法条件,体谓句的陈述关系,主要是由两个单独体词间的并列、偏正关系,因修饰语的参与转化而来的。从语义角度说,体谓句中主谓两部分的逻辑关系、语义制约,以类的形式出现,是句子赖以存在的基础。     

Estimation of critical points in the mixture inverse Gaussian model

The maximum likelihood estimation for the critical points of the failure rate and the mean residual life function are presented in the case of mixture inverse Gaussian model. Several important data sets are analyzed from this point of view. For each of the data sets, Bootstrapping is used to construct confidence intervals of the critical points.     

同类异质产品市场博弈Nash均衡最优策略模型

本文按照Nash均衡解的要求,建立同类异质产品市场用户需求分布及效用结构模型,导出不同定位的企业所实施竞争策略的若干最优条件,通过计算不同策略设计下产品相应的临界功能效用值,参与竞争的企业可找到适合于市场需求的最优决策。     

中国股市收益率分布函数研究

本文在考察了文献中描述股票收益率的各类分布函数的基础上,以稳定Paretian分布与t分布为备择,研究了沪、深股市各类综指收益率的分布函数的形式,并对分布函数的参数进行了估计。     

基于模糊规划的QFD 系统参数确定方法

针对QFD 系统的内在模糊性,运用带有对称三角形模糊系数的模糊规划理论,提出了一 种确定QFD 系统参数的方法. 并通过工程特性目标值的规范化,定义产品开发总成本函数、工 程特性改进成本函数及改进成本系数等概念,建立了一个QFD 规划模型. 仿真结果表明,该模 型能够帮助开发人员在不确定的、模糊条件下有效确定关联函数及自相关函数,优化顾客需求 的满意水平,确定工程特性目标值,使新开发/ 改进的产品顾客满意度赶上或超过目标市场上 的竞争企业,并满足开发预算约束.     

Penalty guided genetic search for redundancy optimization in multi-state series-parallel power system

This paper presents a genetic algorithm (GA) for parallel redundancy optimization in series-parallel power systems exhibiting multi-state behavior, optimizing the reliability subject to constraints. The components are binary and chosen from a list of products available in the market, and are being characterized by their feeding capacity, reliability, cost and weight. System reliability is defined as the ability to satisfy consumer demand and is presented as a piecewise cumulative load curve. In GA, to handle infeasible solutions penalty strategies are used. Penalty technique keep a certain amount of infeasible solutions in each generation so as to enforce genetic search towards an optimal solution from sides of, both, feasible and infeasible regions. We here present a dynamic adaptive penalty function which helps the algorithm to search efficiently for optimal/near optimal solution. To evaluate system reliability, a fast procedure, based on universal generating function, is used. An example considering a multi-state series-parallel power system is solved considering both homogeneous and heterogeneous types of redundancy. Also an example considering price discounts is solved. The effectiveness of the penalty function and the proposed algorithm is studied and shown graphically.     

One-dimensional optimal bounded-shape partitions for Schur convex sum objective functions

Consider the problem of partitioning n nonnegative numbers into p parts, where part i can be assigned n_i numbers with n_i lying in a given range. The goal is to maximize a Schur convex function F whose ith argument is the sum of numbers assigned to part i. The shape of a partition is the vector consisting of the sizes of its parts, further, a shape (without referring to a particular partition) is a vector of nonnegative integers (n₁,..., n_p) which sum to n. A partition is called size-consecutive if there is a ranking of the parts which is consistent with their sizes, and all elements in a higher-ranked part exceed all elements in the lower-ranked part. We demonstrate that one can restrict attention to size-consecutive partitions with shapes that are nonmajorized, we study these shapes, bound their numbers and develop algorithms to enumerate them. Our study extends the analysis of a previous paper by Hwang and Rothblum which discussed the above problem assuming the existence of a majorizing shape. This research is partially supported by ROC National Science grant NSC 92-2115-M-009-014.     

测试实数编码遗传算法的困难度

分析了遗传算法困难度测试在遗传算法研究中的重要意义. 鉴于当前这方面的研究集 中于二进制编码遗传算法,对实数编码遗传算法的困难度测试进行了分析. 探讨了实数编码遗 传算法困难度分析的适应值与距离相关系数测试法与基于随机游走模型的相关函数测试法, 提出了最佳一阶函数逼近测试法,做了大量实验,并根据实证分析结果对三种方法进行了比较 与评价.     

生产函数与成本函数的关系研究

本文给出了生产函数与成本函数之间的一般关系,并证明齐次生产函数与齐次成本函数之间存在着一种齐次对应关系:齐次生产函数在厂商的成本最小化决策下必然产生齐次的成本函数且齐次成本函数必然产生对应于齐次的生产函数。