Measuring Tail Thickness to Estimate the Stable Index α: A Critique

A generalized Pareto or simple Pareto tail-index estimate above 2 has frequently been cited as evidence against infinite-variance stable distributions. It is demonstrated that this inference is invalid; tail index estimates greater than 2 are to be expected for stable distributions with α as low as 1.65. The nonregular distribution of the likelihood ratio statistic for a null of normality and an alternative of symmetric stability is tabulated by Monte Carlo methods and appropriately adjusted for sampling error in repeated tests. Real stock returns yield a stable α of 1.845 and reject iid normality at the .996 level.     

A mixed GWMA–CUSUM control chart for monitoring the process mean

The memory-type control charts are widely used in the process and service industries for monitoring the production processes. The reason is their sensitivity to quickly react against the small process disturbances. Recently, a new cumulative sum (CUSUM) chart has been proposed that uses the exponentially weighted moving average (EWMA) statistic, called the EWMA–CUSUM chart. Similarly, in order to further enhance the sensitivity of the EWMA–CUSUM chart, we propose a new CUSUM chart using the generally weighted moving average (GWMA) statistic, called the GWMA–CUSUM chart, for efficiently monitoring the process mean. The GWMA–CUSUM chart encompasses the existing CUSUM and EWMA–CUSUM charts. Extensive Monte Carlo simulations are used to explore the run length profiles of the GWMA–CUSUM chart. Based on comprehensive run length comparisons, it turns out that the GWMA–CUSUM chart performs substantially better than the CUSUM, EWMA, GWMA, and EWMA–CUSUM charts when detecting small shifts in the process mean. An illustrative example is also presented to explain the implementation and working of the EWMA–CUSUM and GWMA–CUSUM charts.     

Risk Finance for Catastrophe Losses with Pareto‐Calibrated Lévy‐Stable Severities

For catastrophe losses, the conventional risk finance paradigm of enterprise risk management identifies transfer, as opposed to pooling or avoidance, as the preferred solution. However, this analysis does not necessarily account for differences between light‐ and heavy‐tailed characteristics of loss portfolios. Of particular concern are the decreasing benefits of diversification (through pooling) as the tails of severity distributions become heavier. In the present article, we study a loss portfolio characterized by nonstochastic frequency and a class of Lévy‐stable severity distributions calibrated to match the parameters of the Pareto II distribution. We then propose a conservative risk finance paradigm that can be used to prepare the firm for worst‐case scenarios with regard to both (1) the firm's intrinsic sensitivity to risk and (2) the heaviness of the severity's tail.     

New control charts for simultaneous monitoring of the mean vector and covariance matrix of multivariate multiple linear profiles

Simultaneous monitoring of the mean vector and covariance matrix in multivariate processes allows practitioners to avoid the inflated false alarm rate that results from using two independent control charts. In this paper, we extend exponentially weighted moving average semicircle and generally weighted moving average semicircle control charts to monitor the mean vector and covariance matrix of multivariate multiple linear regression profiles in Phase II simultaneously. These new control charts are compared with the existing control charts in the literature in terms of the average run length criterion. Finally, a case is considered to show the application of the proposed charts.     

基于观测状态的中立型时滞系统的镇定控制

研究了基于观测状态的中立型时滞系统的镇定控制问题.给出了新的镇定法则,利用改进的Lyapunov泛函,得到了这类系统基于线性矩阵不等式的镇定条件.最后,用实例说明了该文所得到的结果是正确的.     

屯垦开发路径下唐代西北边疆安全体系的构建

西域在唐代国家安全战略中处于重要地位,因此唐代统治者非常重视唐代西北边疆安全体系的建设。在治理策略上,先是进行屯垦固边活动,有效促进了边疆开发和社会稳定;在此基础上,进行合理的制度建设,实行因地制宜的行政管辖;在屯垦开发的民族合作中,中华民族文化认同逐步增强,以汉文化为主体的多元文化有效促进了民族融合。由此,在唐朝管辖西域的一个多世纪中,有效保障了丝绸之路和西北边疆安全,大唐盛世局面进一步繁荣发展。     

Reparameterization of nonlinear statistical models: a case study

The importance of finding appropriate parameterizations for nonlinear statistical models is highlighted. The purpose of this paper is to explore the principles of reparameterization, using an example from real data. It is shown that stable parameterizations allow likelihood-based confidence intervals to be computed. Further, it is noted that the choice of error distribution may seriously affect the estimates and confidence intervals of quantities of interest. The influence of each observation on the estimation of each parameter is displayed for each error model. Multidimensional likelihood contours may be displayed pairwise using profile likelihood computations.     

协同创新、知识溢出的演化博弈机制研究

基于演化博弈理论,研究企业、大学和科研机构间协同创新过程的"演化稳定策略"。通过设计知识共享模型分析知识投入与知识溢出对协同创新的影响并进行仿真检验。研究认为,长期的协同创新中"合作"策略是参与方采用的"演化稳定策略";当参与方数量不同时,小群体一方率先实现"合作"策略稳定,群体数量相近时双方采用"合作"策略的收敛速度趋于一致;增加知识溢出有利于提高协同创新效率与稳定性。在理论上解释了协同创新博弈的合作策略稳定性,为产学研合作的机制设计提供决策参考。     

关于斜Laplace分布与Levy偏稳定分布的性质

目前有关重尾或偏态数据的统计分析和理论模型相对较少,基于传统的Laplace分布,提出一种处理偏态和重尾数据的新模型——斜Laplace分布,以研究其参数估计方法。利用数理统计知识推导出该分布与一些常见分布(如正态分布、指数分布)间的统计关系,并给出一种可通过设置不同参数值得到不同分布的Levy偏稳定分布及其稳定性。     

县域间土地供给竞合关系演化博弈模型

基于经济发达县域与经济不发达县域在土地供给中的竞合关系,构建演化博弈模型;在模型求解基础上,根据不同典型情形分析演化稳定策略的走向与收敛趋势。研究结果表明,县域政府在土地供给中是否采取相互合作的策略,很大程度上取决于上级政府的监察力度、自身的产业增值收益和基础设施建设成本。