Optimal Threshold Determination for the Maximum Product of Spacing Methodology with Ties for Extreme Events

Extreme events are defined as values of the event below or above a certain value called threshold. A well chosen threshold helps to identify the extreme levels. Several methods have been used to determine threshold so as to analyze and model extreme events. One of the most successful methods is the maximum product of spacing (MPS). However, there is a problem encountered while modeling data through this method in that the method breaks down when there is a tie in the exceedances. This study offers a solution to model data even if it contains ties. To do so, an optimal threshold that gives more optimal parameters for extreme events, was determined. The study achieved its main objective by deriving a method that improved MPS method for determining an optimal threshold for extreme values in a data set containing ties, estimated the Generalized Pareto Distribution (GPD) parameters for the optimal threshold derived and compared these GPD parameters with GPD parameters determined through the standard MPS model. The study improved maximum product of spacing method and used Generalized Pareto Distribution (GPD) and Peak over threshold (POT) methods as the basis of identifying extreme values. This study will help the statisticians in different sectors of our economy to model extreme events involving ties. To statisticians, the structure of the extreme levels which exist in the tails of the ordinary distributions is very important in analyzing, predicting and forecasting the likelihood of an occurrence of the extreme event.

Optimal Threshold Determination for Securities Exchange Volumes Using Improved Maximum Product of Spacing Methodology

To Statisticians, the structure of the extreme levels which exist in the tails of the ordinary distributions is very important in analyzing, predicting and forecasting the likelihood of an occurrence of extreme event. Extreme events are defined as values of the event below or above a certain value called threshold. A well chosen threshold helps to identify the extreme levels. Several methods have been used to determine threshold so as to analyze and model extreme events. One of the most successful methods is the maximum product of spacing (MPS). However, there is a problem encountered while modeling data through this method in that the method breaks down when there is a tie in the exceedances. This study offers a solution to model data even when it contains ties. In the study, a method that improved MPS method for determining an optimal threshold for extreme values in a data set containing ties was derived. The Generalized Pareto Distribution (GPD) parameters for the optimal threshold were derived and compared to GPD parameters determined through the standard MPS model. The study improved the standard MPS methodology by introducing the concept of frequency and used Generalized Pareto Distribution (GPD) and Peak over threshold (POT) methods as the basis of identifying extreme values. The improved MPS models and the standard models were applied to Nairobi Securities Exchange (NSE) trading volume data to determine the GPD parameters for different sectors registered in NSE market and their performance compared. It was realized that the improved MPS model performed better than the standard models. This study will help the Statisticians in different sectors of our economy to model extreme events involving ties.

The deconvolution of lunar brightness temperature based on the maximum entropy method using Chang'e-2 microwave data

A passive and multi-channel microwave sounder onboard the Chang＇e-2 orbiter has successfully acquired microwave observations of the lunar surface and subsurface structure. Compared with the Chang＇e-1 orbiter, the Chang＇e-2 orbiter obtained more accurate and comprehensive microwave brightness temperature data, which are helpful for further research. Since there is a close relationship between mi- crowave brightness temperature data and some related properties of the lunar regolith, such as the thickness, temperature and dielectric constant, precise and high resolution brightness temperature data are necessary for such research. However, through the detection mechanism of the microwave sounder, the brightness temperature data ac- quired from the microwave sounder are weighted by the antenna radiation pattern, so the data are the convolution of the antenna radiation pattern with the lunar brightness temperature. In order to obtain the real lunar brightness temperature, a deconvolution method is needed. The aim of this paper is to solve the problem associated with per- forming deconvolution of the lunar brightness temperature. In this study, we introduce the maximum entropy method （MEM） to process the brightness temperature data and achieve excellent results. The paper mainly includes the following aspects： first, we introduce the principle of the MEM; second, through a series of simulations, the MEM has been verified as an efficient deconvolution method; and third, the MEM is used to process the Chang＇e-2 microwave data and the results are significant.

On an Application of the Improved Maximum Product Criterion to Inverse Acoustic Scattering in a Layered Medium

In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well known factorization method, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a mixed reciprocity principle, which renders the computation of the Green function at the background medium unnecessary. Moreover, to further refine our inversion algorithm, an efficient Tikhonov parameter choice technique, called Improved Maximum Product Criterion (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no a priori knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.

Product Spacing of Stress–Strength under Progressive Hybrid Censored for Exponentiated-Gumbel Distribution

Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained.This paper deals with estimation of the stress strength reliability model R=P(Y<X)when the stress and strength are two independent exponentiated Gumbel distribution random variables with different shape parameters but having the same scale parameter.The stress–strength reliability model is estimated under progressive Type-II hybrid censoring samples.Two progressive Type-II hybrid censoring schemes were used,Case I:A sample size of stress is the equal sample size of strength,and same time of hybrid censoring,the product of spacing function under progressive Type-II hybrid censoring schemes.Case II:The sample size of stress is a different sample size of strength,in which the life-testing experiment with a progressive censoring scheme is terminated at a random time T 2 e0;1T.The maximum likelihood estimation and maximum product spacing estimation methods under progressive Type-II hybrid censored samples for the stress strength model have been discussed.A comparison study with classical methods as the maximum likelihood estimation method is discussed.Furthermore,to compare the performance of various cases,Markov chain Monte Carlo simulation is conducted by using iterative procedures as Newton Raphson or conjugate-gradient procedures.Finally,two real datasets are analyzed for illustrative purposes,first data for the breaking strengths of jute fiber,and the second data for the waiting times before the service of the customers of two banks.

Scientific data products and the data pre-processing subsystem of the Chang'e-3 mission

The Chang＇e-3 （CE-3） mission is China＇s first exploration mission on the surface of the Moon that uses a lander and a rover. Eight instruments that form the scientific payloads have the following objectives： （1） investigate the morphological features and geological structures at the landing site; （2） integrated in-situ analysis of minerals and chemical compositions; （3） integrated exploration of the structure of the lunar interior; （4） exploration of the lunar-terrestrial space environment, lunar sur- face environment and acquire Moon-based ultraviolet astronomical observations. The Ground Research and Application System （GRAS） is in charge of data acquisition and pre-processing, management of the payload in orbit, and managing the data products and their applications. The Data Pre-processing Subsystem （DPS） is a part of GRAS. The task of DPS is the pre-processing of raw data from the eight instruments that are part of CE-3, including channel processing, unpacking, package sorting, calibration and correction, identification of geographical location, calculation of probe azimuth angle, probe zenith angle, solar azimuth angle, and solar zenith angle and so on, and conducting quality checks. These processes produce Level 0, Level 1 and Level 2 data. The computing platform of this subsystem is comprised of a high-performance computing cluster, including a real-time subsystem used for processing Level 0 data and a post-time subsystem for generating Level 1 and Level 2 data. This paper de- scribes the CE-3 data pre-processing method, the data pre-processing subsystem, data classification, data validity and data products that are used for scientific studies.

Ordered product expansions of operators (AB)^±m with arbitrary positive integer

We arrange quantum mechanical operators ■ in their normally ordered product forms by using Touchard polynomials.Moreover,we derive the anti-normally ordered forms of ■ by using special functions as well as Stirling-like numbers together with the general mutual transformation rule between normal and anti-normal orderings of operators.Further,the Q-and P-ordered forms of(QP)±m are also obtained by using an analogy method.

Asymptotic Results for Goodness-of-Fit Tests Using a Class of Generalized Spacing Methods with Estimated Parameters

A class of pseudo distances is used to derive test statistics using transformed data or spacings for testing goodness-of-fit for parametric models. These statistics can be considered as density based statistics and expressible as simple functions of spacings. It is known that when the null hypothesis is simple, the statistics follow asymptotic normal distributions without unknown parameters. In this paper we emphasize results for the null composite hypothesis: the parameters can be estimated by a generalized spacing method (GSP) first which is equivalent to minimize a pseudo distance from the class which is considered;subsequently the estimated parameters are used to replace the parameters in the pseudo distance used for estimation;goodness-of-fit statistics for the composite hypothesis can be constructed and shown to have again an asymptotic normal distribution without unknown parameters. Since these statistics are related to a discrepancy measure, these tests can be shown to be consistent in general. Furthermore, due to the simplicity of these statistics and they come a no extra cost after fitting the model, they can be considered as alternative statistics to chi-square statistics which require a choice of intervals and statistics based on empirical distribution (EDF) using the original data with a complicated null distribution which might depend on the parametric family being considered and also might depend on the vector of true parameters but EDF tests might be more powerful against some specific models which are specified by the alternative hypothesis.

Prediction of Short-Term Distributions of Load Extremes of Offshore Wind Turbines

This paper proposes a new methodology to select an optimal threshold level to be used in the peak over threshold （POT） method for the prediction of short-term distributions of load extremes of offshore wind turbines. Such an optimal threshold level is found based on the estimation of the variance-to-mean ratio for the occurrence of peak values, which characterizes the Poisson assumption. A generalized Pareto distribution is then fitted to the extracted peaks over the optimal threshold level and the distribution parameters are estimated by the method of the maximum spacing estimation. This methodology is applied to estimate the short-term distributions of load extremes of the blade bending moment and the tower base bending moment at the mudline of a monopile-supported 5MW offshore wind turbine as an example. The accuracy of the POT method using the optimal threshold level is shown to be better, in terms of the distribution fitting, than that of the POT methods using empirical threshold levels. The comparisons among the short-term extreme response values predicted by using the POT method with the optimal threshold levels and with the empirical threshold levels and by using direct simulation results further substantiate the validity of the proposed new methodology.

Unified Asymptotic Results for Maximum Spacing and Generalized Spacing Methods for Continuous Models

Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MSP method has been shown to be very useful for estimating parameters for univariate continuous models with a shift at the origin which are often encountered in loss models of actuarial science and extreme models. The MSP estimators have also been shown to be as efficient as maximum likelihood estimators in general and can be used as an alternative method when ML method might have numerical difficulties for some parametric models. Asymptotic properties are presented in a unified way. Robustness results for estimation and parameter testing results which facilitate the applications of the GSP methods are also included and related to quasi-likelihood results.

新质生产力:指标构建与时空演进

新质生产力作为一个全新的概念,为中国的经济和社会发展指明了新的方向,对其内涵与意义的深度发掘至关重要。文章基于生产力的三大构成要件,在挖掘新质生产力长远要求原则下构建其综合评价指标体系,并运用熵值法对中国省域新质生产力发展水平进行测度。研究发现:(1)新质生产力从总体上呈增长趋势,但在南北、四大区域和五大经济带存在显著时空差异;(2)新质生产力在省域之间呈现梯度提升和发展不均衡特点;(3)分维度发现,生产资料对新质生产力提升的贡献度最高,劳动者维度的贡献最低且存在空间极化现象;(4)新质生产力具有显著的集聚效应,主要表现为低-低集聚和高-高集聚,并具有时空收敛性特征。进而提出优化人力资本结构、发挥新质生产力集聚效应和健全区域协调发展机制等政策建议。本文或可加深对中国新质生产力的时空发展格局的认知,为新质生产力培育进而促进经济高质量发展提供新思路。

基于波束空间交替投影极大似然的拖曳式诱饵分辨判别方法

机载平台在遭遇威胁时,通过释放拖曳式诱饵假目标干扰进行自卫.载机和拖曳式诱饵在雷达波束宽度内,且径向距离小于距离分辨率时,雷达无法通过常规方法对载机目标和拖曳式诱饵进行分辨测量.针对数字相控阵雷达同拖曳式诱饵对抗的问题,提出一种基于波束空间交替投影极大似然(BSAP-ML)方法.首先通过阵元空间到波束空间处理,减少数字相控阵维度;然后通过交替投影方法对目标和拖曳式诱饵的角度进行迭代测量;最后通过基于角度向量的判别方法对载机目标和诱饵进行判断识别.仿真结果表明,该方法可用于数字相控阵雷达,对载机和拖曳式诱饵进行有效的超分辨角度测量和判别.

3D矢量空间和最优最劣法在绿色产品设计决策方法中的应用

为了解决目前绿色产品设计方案中产品基础属性考虑欠缺,以及缺乏可视化比较方法的问题,提出一种基于3D矢量空间和最优最劣法(Best worst method,BWM)的绿色产品设计多属性决策方法。通过功能、外观和可持续3个维度为绿色产品设计的基础属性构建3D矢量空间,并对每个维度扩充其包含的下级属性;利用间隔方法优化的BWM获得三个维度及各维度下级属性的权重分配;通过3D矢量空间求得各备选方案的总体评价得分,实现客观科学的绿色产品设计多属性决策。以电动汽车的绿色产品设计方案为例,验证了所提方法的可行性和有效性。

时空视角下城市轨道交通细分产品内涵及形成过程探析

时空关系研究是经济学中探讨运输行为的重要抓手,由于从运输空间位移、商业消费时间耗费和城市空间规则等不同维度,难以系统研究城市轨道交通产品,而经济学的时空转换概念进一步丰富了时空视角下城市轨道交通细分产品的内涵,形成以“运输时间节约量”衡量的运输服务产品(Pt)、以“消费时间增加量”衡量的商业服务产品(Pc)和以“要素流动时间节约量”衡量的城市服务产品(Pu)。在此基础上,从生产过程分析、细分产品间关系及生产组织行为等维度,分析了时空视角下城市轨道交通细分产品形成过程,提出时空视角下城市轨道交通细分产品分析方法应用,即:合理确定网络生产规模,构建分层观察网络生产行为,明确TOD模式发展方向,提升城轨网络生产效率。

基于状态空间法的平面圆弧曲梁面外动力学分析

该文通过选择广义位移和与其对偶的广义力作为状态变量,建立了平面圆弧曲梁面外动力学问题的状态方程列式,并求解了工程中常见的四种边界条件下圆弧曲梁面外自由振动的频率和模态。利用状态空间列式和辛内积的概念,建立了振动模态关于质量和旋转惯量以及关于刚度的正交关系式。基于建立的振动模态关于质量和旋转惯量的正交关系式,运用模态叠加法得到了非齐次状态方程即面外强迫振动控制方程的解析解,并具体考察了竖向移动荷载作用下圆弧曲梁的动力响应。给出了数值算例,并与已有结果进行了比较,验证了该文方法在进行圆弧曲梁面外自由振动和强迫振动分析时的准确性和可靠性。

嘉兴市南湖区“三生空间”研究

重点分析了现阶段国内“三生空间”的分类体系和研究方法,以“三生空间”内涵、第三次国土调查工作分类为基础,以土地利用主导功能为根据,结合研究区的土地利用特征确定“三生空间”的土地利用分类体系。采用第三次国土调查时点更新成果为基础数据,利用多样性指数、区位商、基尼系数等多个指标探讨了研究区生产-生活-生态用地的空间结构特征,提出了相应的土地利用和土地管理对策,为未来研究区国土空间规划和可持续发展提供依据。

河南省优势粮食作物生产空间布局研究

【目的】探究河南省优势粮食作物生产空间布局,确定粮食作物生产优劣分区,为优化河南省粮食生产的空间布局、调整粮食结构发展方向提供理论支持。【方法】基于2011—2020年粮食生产数据,利用重心模型、标准差椭圆研究河南省优势粮食作物生产格局变化,再借助比较优势指数法对水稻、小麦、玉米和大豆进行比较优势分析,通过比较优势指数对河南省18个市在粮食生产力和生产规模方面进行分析,从而确定优劣粮食产区。【结果】(1)水稻和玉米生产重心往东南方向迁移,小麦生产重心往西南方向迁移,大豆生产重心往西北方向迁移,优势粮食作物自北向南呈现出“小麦-玉米-大豆-水稻”的分布格局。水稻生产空间变化呈现向南集聚的趋势,小麦呈现向东南集聚的趋势,大豆呈现向西北集聚的趋势。(2)河南省优势粮食作物生产存在明显的比较优势差异。小麦生产具有明显的比较优势,水稻和大豆具有明显的比较劣势。(3)河南省水稻优势产区2个,小麦优势产区10个,玉米优势产区14个,大豆优势产区11个。【结论】在保证粮食作物播种面积不变的基础上还要通过加大粮食生产的投入力度来提高粮食作物单位面积产量,从而实现农业资源利用最大化;因地制宜,合理调整河南省各市粮食作物的种植结构和空间布局;结合自身优势完善农业政策,大力推进向优势产区集聚的发展模式。

基于数据驱动的油藏流场重构方法

多层碎屑岩油藏稳油控水一直是油田开发的热点问题,油田进入中—高含水期后产油量下降明显,平面剩余油分布零散,层间开发矛盾突出,迫切需要合适的优化调控方法使其持续稳产。根据贝叶斯后验概率方法与油藏流线模拟器,应用随机极大似然函数求解历史拟合问题并构建数据空间集,利用有限记忆的拟牛顿梯度方法来反演数据空间集与推测未来,综合Pollock流线追踪方法表征油藏流场的瞬时流动速度,提出了一种基于数据空间反演的油藏流场重构方法。此方法无需复杂重复的运算就可实现油藏注采参数的实时优化,突破了传统优化方法无法精细描述流场演变的局限性,弥补了数据空间反演在流场优化方面应用的空白。以渤海B油藏为例,利用基于数据空间反演的油藏流场重构方法,揭示了油藏注采结构优化的运行机理,直观展示了油藏流场优化的实现过程。现场调控结果显示,油藏综合含水率较为稳定,调控井组单元零散状剩余油被有效动用,水驱波及面积扩大24.85%,油藏流体疏导效果显著。这些油藏数字化探索与实践,将为同类中—高含水期油田开发与数据驱动油藏流场调控的应用提供借鉴。

基于状态空间法的圆弧曲梁面内动力学分析

该文采用状态空间法研究了圆弧曲梁面内动力学特性。通过选择合适的状态变量,建立了相应的状态空间列式,并给出了固有频率和振动模态的求解过程。进一步通过引入辛内积的概念,建立了三种工程常见边界条件(简支、固支和自由)下圆弧曲梁面内振动模态关于质量和旋转惯量的正交关系式。在此基础上,运用模态叠加法给出了非齐次状态方程的解析解,并得到了圆弧曲梁在竖向移动集中荷载作用下的瞬态响应。数值算例结果表明该文方法是十分精确和可靠的。

考虑多影响因素的配筋UHPC梁裂缝宽度计算方法

为建立适用于配筋超高性能混凝土(UHPC)梁的裂缝宽度计算方法,对8片UHPC-T形梁开展了四点抗弯试验,分析钢纤维体积分数、配筋率及保护层厚度对裂缝宽度的影响规律.基于钢筋-UHPC协同受力和变形协调机理,采用半理论半经验法构建了能综合反映多影响因素的最大裂缝宽度计算公式,并提出了适用于UHPC梁的钢筋应力、应变不均匀系数及平均裂缝间距计算方法.结果表明:在试验范围内,裂缝宽度随纤维体积分数、配筋率的提高而减小,随保护层厚度增加而增大;UHPC梁的钢筋应变不均匀程度大于普通混凝土梁;平均裂缝间距计算值与文献实测值最大相对误差为11.17%,最大裂缝宽度计算值与实测值、文献实测值之比的均值分别为1.02、1.01,变异系数分别为0.05、0.12,表明所提出公式可准确计算配筋UHPC梁的最大裂缝宽度.