Maximum likelihood estimator of the parameter for a continuous one-parameter exponential family under the optimal ranked set sampling

This paper studies a maximum likelihood estimator (MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling (RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed (iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice, are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.     

熵损失函数下广义指数分布的可靠性估计

在广义指数分布场合下, 讨论了其参数、可靠性指标的估计及性质. 基于熵损失函数, 在共轭先验分布下, 通过对分布函数进行变换, 获得了该分布参数、可靠性指标的 UMVUE、最小风险同变估计、Bayes 估计和经验 Bayes 估计, 并证明了形如 [cT(x) + d]^-1 的一类估计的容许性. 最后运用 Monte-Carlo 方法对各种估计的 MSE 进行了模拟比较. 结果表明, 经验贝叶斯估计精度较高.     

A one-parameter filled function for nonsmooth global optimization and its application

This paper presents a modified definition of the filled function for finding a global minimizer of a nonsmooth function on a closed bounded set, and then give a one-parameter filled function. Theoretical and numerical properties of the proposed filled function are investigated and a corresponding solution algorithm is proposed. The proposed filled function’s parameter is easier to be appropriately chosen than previous functions in literatures. Numerical results obtained indicate the efficiency of the proposed filled function method. An improved fingerprint recognition method using global filled function is also reported.     

Exponential stability of linear distributed parameter switched systems with time-delay

In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems (DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS’ exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities (LOIs) where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.     

时滞分布参数系统的指数渐近稳定性

基于Lyapunov稳定性理论,利用辅助函数方法研究由变时滞分布参数控制系统所导出的滑动模运动方程的指数渐近稳定性问题,获得了一类滑动模运动方程指数渐进稳定的充分条件,建立了滑动模运方程解的指数渐近稳定性定理。这就为研究时滞分布参数系统的变结构控制问题奠定了理论基础。     

含时间周期项的离散灰色DGM(1,1,T)模型及其应用

针对系统行为序列的周期性波动特征，将三角函数引入离散灰色预测模型，提出含时间周期项的离散灰色DGM（1，1，T）模型，其还原公式可表示为三角函数和指数函数的耦合形式，从而表明该模型适用于既存在周期性又具有趋势性的复合型序列.基于最小二乘思想，将DGM（1，1，T）模型的参数估计转化为非线性优化问题，并提出PSO-LM混合算法进行数值求解；通过数值实验对模型的适用范围和参数估计方法的有效性进行验证；最后将该模型应用于河南省安阳市、洛阳市、许昌市和商丘市的农业干旱预测，结果表明2019年四个地市的土壤湿度将呈现出下降态势.     

基于屏蔽数据多重定数截尾下系统部件的可靠性估计

利用屏蔽的系统寿命数据,在多重定数截尾样本下研究串联系统中部件的可靠性估计问题。首先利用概率元分析方法,推导样本似然函数。然后基于样本似然函数,给出部件参数和可靠度函数的极大似然估计,同时分别在平方损失、线性指数损失和广义熵损失下,得到了部件参数和可靠度函数的Bayes估计。最后通过数值仿真研究屏蔽水平和截尾因子对估计精度的影响,并对各种估计进行了比较。     

GM（1，1，β）灰微分方程的若干性质

针对灰色预测模型的适应范围和优化问题,首先根据灰色GM（1,1）模型参数是灰的、可调的原理,提出了GM（1,1,β）模型的内涵型和参数包形式,分析了模型的若干性质,然后给出了模型的优化算法. 研究结果表明,GM（1,1,β）灰微分方程模型参数α的客观取值范围为（-∞,+∞）,经典GM（1,1）模型参数α的客观取值范围为（-2,+2）;发展系数α的客观取值范围是由背景值系数β 决定的,而与原始数据无关;灰微分方程模型完全适合齐次指数数列. 最后,以我国城镇居民家庭人均可支配收入的数据为例验证了GM（1,1,β）灰微分方程模型的有效性.     

新的单参数混沌振子网络的同步化区域的转迁

本文针对一个新发现的单参数混沌系统作为节点动力学的动力网络，在给定某一内连矩阵情况下，研究了随节点动力学参数的连续变化，复杂动力网络同步化区域的演化与切换. 我们把这种网络同步化区域随节点动力学参数发生变化的现象称为网络同步化区域的分岔或转迁. 结果发现，对于某些内连矩阵，同步化区域不产生分岔现象，表明网络同步状态的稳定性不会因节点动力学参数的变化而发生改变；而对于某些内连矩阵，随节点动力学参数的逐渐增大，同步化区域主要出现了下面几种分岔或转迁模式：（1）无界-空集型的，（2）空集-有界-无界-有界-无界型的，（3）空集-无界-空集-无界-空集-无界型的，（4）空集-有界-无界-有界界-无界型的. 在这些分岔模式中，同步化区域随动力学参数的增大最后大都演化成无界型的，与统一混沌系统为节点动力学的网络的同步化区域的分岔模式有着显著差异. 这些现象表明：同一类型的节点动力学，不同的内连矩阵，矩阵网络同步化区域的分岔模式是不一样的；同一内连矩阵，不同类型的节点动力学，网络的同步区域的分岔模式也存在很多差异；不同的分岔模式，网络同步状态的稳定性也是不一样，它势必影响网络的同步能力.     

Processing for Zero-Failure Data of the Products

1 .ＩＮＴＲＯＤＵＣＴＩＯＮＩｎｔｈｅｔｉｍｅｅｎｄｅｄｒｅｌｉａｂｉｌｉｔｙｔｅｓｔｓ,ｔｈｅｐｒｏｂｌｅｍｏｆｚｅｒｏ ｆａｉｌｕｒｅｄａｔａｉｓｅｎｃｏｕｎｔｅｒｅｄｓｏｍｅｔｉｍｅｓ ,ｅｓｐｅｃｉａｌｌｙｉｎｈｉｇｈ ｒｅｌｉａｂｉｌｉｔｙａｎｄｓｍａｌｌｓａｍｐｌｉｎｇｔｅｓｔｓ .Ｔｈｅｚｅｒｏ ｆａｉｌｕｒｅｄａｔａｒｅｓｅａｒｃｈｉｓａｎｅｗｆｉｅｌｄｉｎｔｈｅｒｅｃｅｎｔｙｅａｒｓ ,ｂｕｔｉｔｉｓｕｒ ｇｅｎｔｌｙｄｅｍａｎｄｅｄｉｎｐｒａｃｔｉｃａｌｐｒｏｊｅｃｔｓ,ｓｏｉｔｈａｓｇ…     

Exponential stability for cellular neural networks: an LMI approach

A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks （DCNNs） is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.     

Optimization of Background Value in GM(1,1) Model

This article has proved that discrete function with homogeneous exponential law will become discrete function with non-homogeneous exponential law if the function with homogeneous exponential law accumulates, while discrete function with homogeneous exponential law is generated by inversely accumulating the discrete function with non-homogeneous exponential law. Based on the error analysis of the model GM(1,1), researchers use the discrete function with non-homogeneous exponential law to fit the accumulated sequence in order to propose a new method for optimizing background value in model GM(1,1). There are plenty of data simulations and models. And it shows that the new model broke through restrictions of using coefficient, and it still improved its matching and prediction precision.     

预测模型参数的指数平滑估计法及其应用的进一步研究

首先提出指数平滑技术在预测模型参数估计中应用的原理,其次研究指数平滑参数估计法的渐近最优性,最后,应用指数平滑技术给出修正指数曲线预测模型参数估计及组合预测确定权重的一类新方法．     

不确定时滞系统的指数稳定保代价可靠控制

针对一类含有时变时滞的不确定参数系统,研究了在执行器发生故障情况下系统指数稳定保代价可靠控制器设计问题。系统的性能函数是含有指数项和故障输入项的积分二次型函数。经过适当的状态变换,将原系统的指数稳定保代价可靠控制问题转化为另一个等价系统的保代价可靠控制问题。根据Lyapunov稳定性理论,得到了系统存在指数稳定保代价可靠控制器应满足的一个矩阵不等式,进一步将这个矩阵不等式转化为线性矩阵不等式(LMI),并给出了系统的保代价表达式。利用论文方法设计的控制器能够使得时滞系统对于任意允许的不确定量以及执行器故障都保持鲁棒可靠指数稳定,并且使系统具有保代价的性能指标。仿真结果表明了该控制器设计方法的有效性。     

灰指数规律的熵判据

研究了函数为指数函数的充要条件 ,并给出了白指数律的判别准则 .在此基础上 ,给出了灰指数律判别方法 ,对于固定的分量增量 ,离散函数的实际熵趋于最大熵时 ,此离散函数具有灰指数律 .与此同时 ,讨论了灰指数函数的灰性测度问题 ,并给出了灰指数函数的灰度公式.     

ASYMPTOTIC PROPERTIES OF MLE IN EXPONENTIAL FAMILY NONLINEAR MODELS

1.IntroductionSupposethattherandomvariablesyi5y2,'',y.areindependentandeachyihasdensity:withrespecttoaa-finitemeasurev,whereb,c,]areknownl'unctions;fiisaknownq-vectordefinedinX,Pistheunknownp-vectorparameterdefinedinB,oiisthenaturalparameter,andaisascaleparameter.Then(1)iscalledtheexponentialfamilynonlinear..dels[2]whicharenaturalextensionofgeneralizedlinearmodelsandnormalnonlinearmodels.Inthispaper,wegeneralizetheasymptoticresultof[1]and[3,4]toexponentialfamilynonlinearmodels.Section2gives…     

Discriminant analysis based on statistical depth

<正> In the past two decades,many statistical depth functions seemed as powerful exploratoryand inferential tools for multivariate data analysis have been presented.In this paper,a new depthfunction family that meets four properties mentioned in Zuo and Serfling(2000)is proposed.Then aclassification rule based on the depth function family is proposed.The classification parameter b couldbe modified according to the type-Ⅰ error α,and the estimator of b has the consistency and achievesthe convergence rate n~(-1/2).With the help of the proper selection for depth family parameter c,theapproach for discriminant analysis could minimize the type-Ⅱ error β.A simulation study and a realdata example compare the performance of the different discriminant methods.     

任意寿命分布单元表决系统备件需求量的解析算法

表决结构广泛存在于装备的可靠性设计中。针对表决系统备件需求计算困难、不准确的问题,提出了一种基于寿命分布等效的表决系统备件需求量计算方法。首先通过R 等效方法将系统中的非指数单元转化为指数单元;而后将多指数单元表决系统等效为伽马系统并给出等效伽马系统参数的经验计算公式;在此基础上以可用度为保障约束指标,利用伽马分布的可加性得到备件计算结果;最后在实际算例中,通过与仿真结果的比较表明,此解析算法对于指数单元具有较高精度,对于非指数单元,在可用度较高的情况下亦能满足精度要求。     

不确定多变量线性系统的快速收敛滑模控制

讨论了一类不确定多变量线性系统滑模变结构控制的快速收敛问题,提出一种指数型快速终端滑模变结构控制方案。通过非奇异线性变换将不确定系统化为简约标准型,而后设计了非线性指数型快速终端滑模超曲面,给出了滑模面参数矩阵的选择方法。在此基础上设计了变结构控制律,使系统状态在有限时间内到达滑模面上,随后保持在滑模面上并按指数型终端滑模的规律运动,在有限时间内收敛到平衡点。与普通的快速终端滑模相比,系统状态能以更短的时间到达平衡点。该方法具有全局稳定性和鲁棒性,仿真结果证明其有效性。     

Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems

Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.