Axiomatizations of the normalized Banzhaf value and the Shapley value

A cooperative game with transferable utilities– or simply a TU-game – describes a situation in which players can obtain certain payoffs by cooperation. A solution concept for these games is a function which assigns to every such a game a distribution of payoffs over the players in the game. Famous solution concepts for TU-games are the Shapley value and the Banzhaf value. Both solution concepts have been axiomatized in various ways. An important difference between these two solution concepts is the fact that the Shapley value always distributes the payoff that can be obtained by the `grand coalition' consisting of all players cooperating together while the Banzhaf value does not satisfy this property, i.e., the Banzhaf value is not efficient. In this paper we consider the normalized Banzhaf value which distributes the payoff that can be obtained by the `grand coalition' proportional to the Banzhaf values of the players. This value does not satisfy certain axioms underlying the Banzhaf value. In this paper we introduce some new axioms that characterize the normalized Banzhaf value. We also provide an axiomatization of the Shapley value using similar axioms. Received: 10 April 1996 / Accepted: 2 June 1997     

高质量发展视域下三级公立医院重大传染病救治能力评价指标体系构建

文章综合运用定性和定量相结合的研究方法,通过文献研究初步拟定评价指标集后, 采用德尔菲法进行两轮专家咨询,并利用层次分析法计算各项指标权重,旨在构建安徽省三级公立医院重大传染病救治能力评价指标体系。结果显示,两轮咨询的专家积极系数分别为 100%、90%,专家权威系数分别为0.825、0.831,肯德尔和谐系数分别为0.123、0.124（P＜0.001）,表明专家咨询的可信度高。最终构建的安徽省三级公立医院重大传染病救治能力评价指标体系包含6个一级指标、15个二级指标、50个三级指标,且具有较高的科学性和可靠性。在公立医院高质量发展视域下,该指标体系可为三级公立医院重大传染病救治能力的考核评估与质量提升提供理论依据。     

短面板随机效应模型的分位数回归方法及模拟

对于随机效应面板数据的分位数回归研究的难点在于如何处理截面内存在的相关性,文章借助分位数回归与ALD分布之间的关系,提出了带有Copula相关结构的分位数回归的极大似然估计法,其中Copula函数可用来表示短面板中的截面内相关性.通过数值优化算法迭代求解目标函数可得参数估计值,蒙特卡洛模拟结果显示该方法的均方误差更小,因此更为精确可靠.     

平行数据模型单位根的非参数检验方法——截面内误差项存在L阶自相关关系

时间序列单位根检验问题是现代经济计量学研究的一个焦点问题。由于平行数据模型研究的是跨横截面的时间序列问题,因此单位根检验问题对它来说也非常重要。这个问题目前在平行数据模型的研究领域备受关注。本文通过研究时间序列单位根的非参数Z检验方法与平行数据模型单位根的IPS检验方法,针对横截面内误差项存在L阶自相关关系的平行数据模型,提出了非参数单位根检验方法;并利用Monte-Carlo方法模拟比较了本文提出方法与LL单位根检验方法的效果。一、时间序列单位根的非参数Z检验方法Phillips(1988)考虑了时间序列可能出现的自相关关系…     

The generalized two-sided power distribution

The generalized standard two-sided power (GTSP) distribution was mentioned only in passing by Kotz and van Dorp Beyond Beta, Other Continuous Families of Distributions with Bounded Support and Applications, World Scientific Press, Singapore, 2004. In this paper, we shall further investigate this three-parameter distribution by presenting some novel properties and use its more general form to contrast the chronology of developments of various authors on the two-parameter TSP distribution since its initial introduction. GTSP distributions allow for J-shaped forms of its pdf, whereas TSP distributions are limited to U-shaped and unimodal forms. Hence, GTSP distributions possess the same three distributional shapes as the classical beta distributions. A novel method and algorithm for the indirect elicitation of the two-power parameters of the GTSP distribution is developed. We present a Project Evaluation Review Technique example that utilizes this algorithm and demonstrates the benefit of separate powers for the two branches of activity GTSP distributions for project completion time uncertainty estimation.     

Dependence Between Two Diagnostic Tests with Copula Function Approach: A Simulation Study

The study of the dependence between two medical diagnostic tests is an important issue in health research since it can modify the diagnosis and, therefore, the decision regarding a therapeutic treatment for an individual. In many practical situations, the diagnostic procedure includes the use of two tests, with outcomes on a continuous scale. For final classification, usually there is an additional “gold standard” or reference test. Considering binary test responses, we usually assume independence between tests or a joint binary structure for dependence. In this article, we introduce a simulation study assuming two dependent dichotomized tests using two copula function dependence structures in the presence or absence of verification bias. We compare the test parameter estimators obtained under copula structure dependence with those obtained assuming binary dependence or assuming independent tests.     

Graphical and Numerical Methods for Detecting Influential Observations in Complex Bingham Data

We describe methods to detect influential observations in a sample of pre-shapes when the underlying distribution is assumed to be complex Bingham. One of these methods is based on Cook's distance, which is derived from the likelihood of the complex Bingham distribution. Other method is related to the tangent space, which is based on the local influence for the multivariate normal distribution. A method to detect outliers is also explained. The application of the methods is illustrated in both a real dataset and a simulated sample.     

Survival Estimation with Missing Censoring Times for the Generalized Koziol–Green Model

ABSTRACT

When analyzing time-to-event data, there are various situations in which right censoring times for unfailed units are missing. In that context, by taking a supplementary sample of a convenient percentage of unfailed units, we propose a semi-parametric method for estimating a survival function under the natural extension of the Koziol–Green model to double random censoring. Some large sample properties of this estimator are derived. We prove uniform strong consistency and asymptotic weak convergence to a Gaussian process. A simulation study is also presented in order to analyze the behavior of the proposed estimator.     

Waiting time to exhaust lottery numbers

Questions related to lotteries are usually of interest to the public since people think there is a magic formula which will help them to win lottery draws. This note shows how to compute the expected waiting time to observe specific numbers in a sequence of lottery draws and show that surprising facts are expected to occur.