The exponential distribution analog of the Grubbs–Weaver method

Abstract

Grubbs and Weaver (1947 Grubbs, F. E., and C. L. Weaver. 1947. The best unbiased estimate of population standard deviation based on group ranges. Journal of the American Statistical Association 42 (238):224–41. doi: 10.2307/2280652.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) suggest a minimum-variance unbiased estimator for the population standard deviation of a normal random variable, where a random sample is drawn and a weighted sum of the ranges of subsamples is calculated. The optimal choice involves using as many subsamples of size eight as possible. They verified their results numerically for samples of size up to 100, and conjectured that their “rule of eights” is valid for all sample sizes. Here we examine the analogous problem where the underlying distribution is exponential and find that a “rule of fours” yields optimality and prove the result rigorously.     

Multi-objective optimization in partitioning the healthcare system of Parana State in Brazil

Motivated by a proposal of the local authority for improving the existing healthcare system in the Parana State in Brazil, this article presents an optimization-based model for developing a better system for patients by aggregating various health services offered in the municipalities of Parana into some microregions. The problem is formulated as a multi-objective partitioning of the nodes of an undirected graph (or network) with the municipalities as the nodes and the roads connecting them as the edges of the graph. Maximizing the population homogeneity in the microregions, maximizing the variety of medical procedures offered in the microregions, and minimizing the inter-microregion distances to be traveled by patients are considered as three objective functions of the problem. An integer-coded multi-objective genetic algorithm is adopted as the optimization tool, which yields a significant improvement to the existing healthcare system map of the Parana State. The results obtained may have a strong impact on the healthcare system management in Parana. The model proposed here could be a useful tool to aid the decision-making in health management, as well as for better organization of any healthcare system, including those of other Brazilian States.     

Resource Distribution in Multiple Attacks with Imperfect Detection of the Attack Outcome

This article extends the previous research of consecutive attacks strategy by assuming that an attacker observes the outcome of each attack imperfectly. With given probabilities it may wrongly identify a destroyed target as undestroyed, and wrongly identify an undestroyed target as destroyed. The outcome of each attack is determined by a contest success function that depends on the amount of resources allocated by the defender and the attacker to each attack. The article suggests a probabilistic model of the multiple attacks and analyzes how the target destruction probability and the attacker's relative resource expenditure are impacted by the two probabilities of incorrect observation, the attacker's and defender's resource ratio, the contest intensity, the number of attacks, and the resource distribution across attacks. We analyze how the attacker chooses the number of attacks, the attack stopping rule, and the optimal resource distribution across attacks to maximize its utility.     

A new metamodel-based method for solving semi-expensive simulation optimization problems

In this article, a new algorithm for rather expensive simulation problems is presented, which consists of two phases. In the first phase, as a model-based algorithm, the simulation output is used directly in the optimization stage. In the second phase, the simulation model is replaced by a valid metamodel. In addition, a new optimization algorithm is presented. To evaluate the performance of the proposed algorithm, it is applied to the (s,S) inventory problem as well as to five test functions. Numerical results show that the proposed algorithm leads to better solutions with less computational time than the corresponding metamodel-based algorithm.     

上海城市人口总量控制与结构优化研究

上海的人口总量和结构一直与其独特的工业化、城镇化进程密不可分。工业化带动人口发展,人口发展推动城市发展。改革开放以来,上海正处于第四波工业化时期,人口增长较快。在人口结构上,户籍人口老龄化,而外来人口具有就近流动、城城流动、定居化特点,且教育水平逐年提高。从承载力上看,上海人口总量合理,但人口分布的不合理影响了人口结构的发展、城市社会的融合,带来了核心区人口过密、产城融合不畅的问题,以及偏好"人脑"、排斥"人手"的问题。面对人口老龄化和可能的人口逆流,上海应稳定人口总量,建设整体推进的多中心发展人口分布格局,完善户籍制度改革,破解"新二元结构",推动社会保障和公共服务均等化,同时结合政府改革,完善相关配套改革措施。     

Multinomial Selection in the Presence of Infinite Alternatives

We propose a new procedure for the multinomial selection problem to solve a real problem of any modern Air Force: the elaboration of better air-to-air tactics for Beyond Visual Range air-to-air combat that maximize its aircraft survival probability H(θ, ω), as well as enemy aircraft downing probability G(θ, ω). In this study, using a low-resolution simulator with generic parameters for the aircraft and missiles, we could increase an average success rate of 16.69% and 16.23% for H(θ, ω) and G(θ, ω), respectively, to an average success rate of 76.85% and 79.30%. We can assure with low probability of being wrong that the selected tactic has greater probability of yielding greater success rates in both H(θ, ω) and G(θ, ω) than any simulated tactic.     

中国决策情境下的多源流模型及其优化研究

作为当今公共政策研究领域最炙手可热的理论模型之一,约翰·金登的多源流分析理论业已得到国内外学者的广泛应用与认可。在对该模型的相关内容进行简单铺陈后,通过辨析国内外不同的政策主体参与逻辑,进一步厘清了我国公共决策的独有特征。研究重点是在整合提炼西方既有修正思路的基础上,沿袭模型的模糊性假设,结合我国具体实践案例,对多源流模型进行优化与补充。研究表明,中国决策情境下的多源流模型优化主要有提高源流间的融合性、政治源流的核心化、焦点事件的独立化以及特殊情况下的临时决策等四种路径,四种优化与补充路径的有机结合将为进一步提升模型适用性提供帮助。     

Particle swarm optimization based Liu-type estimator

In this study, a new method for the estimation of the shrinkage and biasing parameters of Liu-type estimator is proposed. Because k is kept constant and d is optimized in Liu’s method, a (k, d) pair is not guaranteed to be the optimal point in terms of the mean square error of the parameters. The optimum (k, d) pair that minimizes the mean square error, which is a function of the parameters k and d, should be estimated through a simultaneous optimization process rather than through a two-stage process. In this study, by utilizing a different objective function, the parameters k and d are optimized simultaneously with the particle swarm optimization technique.     

Modified genetic algorithm-based clustering for probability density functions

This article modifies two internal validity measures and applies them to evaluate the quality of clustering for probability density functions (pdfs). Based on these measures, we propose a new modified genetic algorithm called GA-CDF to establish the suitable clusters for pdfs. The proposed algorithm is tested by four numerical examples including two synthetic data sets and two real data sets. These examples illustrate the superiority of proposed algorithm over some existing algorithms in evaluating the internal or external validity measures. It demonstrates the feasibility and applicability of the GA-CDF for practical problems in data mining.     

On algorithmic construction of maximin distance designs

Maximin distance designs are useful for conducting expensive computer experiments. In this article, we compare some global optimization algorithms for constructing such designs. We also introduce several related space-filling designs, including nested maximin distance designs, sliced maximin distance designs, and general maximin distance designs with better projection properties. These designs possess more flexible structures than their analogs in the literature. Examples of these designs constructed by the algorithms are presented.