On compounded bivariate poisson distributions

A unified treatment is given for a class of discrete distributions derived by compounding a bivariate Poisson with a bivariate discrete or continuous distribution. Using generating functions a number of interesting results are obtained for probabilities, moments, cumulants, factorial moments, and factorial cumulants. Conditional distributions and regression functions are also examined. Five illustrative examples are presented in detail. © 1994 John Wiley & Sons, Inc.     

On the bivariate negative binomial distribution of mitchell and paulson

The bivariate negative binomial distribution of Mitchell and Paulson [17] for the case b = c = 0 is shown to be equivalent to the accident proneness model of Edwards and Gurland [4] and Subrahmaniam [19,20]. The diagonal series expansion of its joint probability function is then derived. Two other formulations of this distribution are also considered: (i) as a mixture model, which showed how it arises as the discrete analogue to the Wicksell-Kibble bivariate gamma distribution, and (ii) as a consequence of the linear birth-and-death process with immigration.     

A bivariate normal theory maximum-likelihood technique when certain variances are known

A maximum-likelihood technique is described for estimating the bivariate normal distribution of the estimates of two or more related values when data are obtained from several different sources, each having known variance. The problem is comparable, in the bivariate sense to estimating the mean of a normal population with known variance. The results tend to be dominated by those sources of data associated with the smallest variances.     

Lower confidence limits for the impact probability within a circle in the normal case

Lower confidence limits are derived for the impact probability within a circle of fixed radius. The bivariate normal distribution with zero means, unequal variances, and zero correlation is the probability model for impacts. A new representation of the impact probability function is offered. This presentation is valid also for the dependent case, where the eigenvalues of the covariance matrix replace the variances. When the ratio of variances is known the lower confidence limits are uniformly most accurate (UMA). A few alternative approaches are compared by simulation when the ratio of variances is unknown.     

A technique which combines modified pattern search methods with composite designs and polynomial constraints to solve constrained optimization problems

This paper presents a method of selecting design parameters which optimizes a specific measure (aircraft design example: minimum weight, maximum mission effectiveness) and guarantees designated levels of response in specified areas (such as combal ceiling, acceleration time). The method employs direct search optimization applied to a nonlinear functional constrained by nonlinear surfaces. The composite design technique is combined with regression methods to determine adequate surface representations with a minimum of required data points. A sensitivity analysis is conducted at the optimum set of design parameters to test for uniqueness.     

固定式超近程防护系统优化设计及统计分析

为了提高固定式超近程防护系统的拦截效率,进一步优化攻击单元的分布参数,将分布方案的分布参数5个射角和35个射向作为自变量,以拦截概率作为因变量,将已有的32种方案的分布方案及统计模拟所得的拦截概率作为样本值,运用SPSS软件进行多元线性回归分析,通过不断筛去显著性比较差的变量,最终得到比较满意、显著性比较强的多元线性回归方程,该方程的建立为进一步优化分布方案的参数提供了理论依据,也为建立进一步优化模型提供了理论基础.     

相依风险下的超额赔款再保险

本文通过求二次效用函数的货币期望效用的最大值来确定自留额，认为索赔次数服从二元泊松分布，超额赔款再保险的保费按期望值原理进行计算。     

M/M/1 queues with interdependent arrival and service processes

We study via simulation an M/M/1 queueing system with the assumption that a customer's service time and the interarrival interval separating his arrival from that of his predecessor are correlated random variables having a bivariate exponential distribution. We show that positive correlation reduces the mean and variance of the total waiting time and that negative correlation has the opposite effect. By using spectral analysis and a nonparametric test applied to the sample power spectra associated with certain simulated waiting times we show the effect to be statistically significant.     

幂函数型完全非线性函数原像分布的特征

完全非线性函数是特征为奇数的有限域上抗差分密码攻击最优的函数,目前已有的六类完全非线性函数都是2-1的。当Π(x)为Fqm上的Dembowski-Ostrom函数或者Coulter-Matthews函数时,从Fqm到Fq的完全非线性函数tr(aΠ(x))的原像分布恰有两种取值,其中一种取值对应Fqm所有平方剩余元,另一种取值对应Fqm所有非平方剩余元。该结论在文中得到了证明。     

基于杂草算法的超磁致伸缩作动器耦合模型识别

考虑磁滞损耗、动态应力等因素的超磁致伸缩作动器磁滞模型可有效揭示电-磁-机-热多场耦合效应,但准确识别其非线性模型往往存在较大困难。智能杂草算法具有激烈的竞争机制和较强的搜索能力,可用于解决作动器多目标物理参数辨识问题。传统算法的种子数量以线性方式产生且分布方差与适应度缺乏联系,极大地影响了算法收敛速度和模型识别精度。为此,提出一种非线性繁殖和分布的混合改进杂草算法,并将其应用于超磁致伸缩作动器模型识别。实验表明:改进算法具有较强的噪声抑制能力,能精确辨识含有噪声扰动的作动器磁滞非线性模型物理参数;模型预测值和实验数据误差较小,所识别参数可使磁滞非线性模型较为全面地描述作动器多场耦合机理和动态特性。     

比例规则后件的T-S模糊模型辨识方法

模糊划分应满足测量准则,这一点常被忽略。采用余弦平方函数作为隶属函数,解决了曲线型隶属函数在模糊化分后满足测量准则问题。T-S模糊模型后件由线性函数构成,以局部线性化方式实现全局非线性,通过分段性逼近辨识曲线,常用于系统辨识中,但其辨识参数多是其主要问题。比例规则后件的T-S模糊系统具有万能逼近特性,且构成参数少,用于非线性系统的辨识中,可以减少辨识参数,提高辨识速度。给出其在系统辨识中应用的方法,并通过仿真实例说明本方法的有效性。     

一种金属橡胶元件建模方法研究

用理论和试验相结合的手段研究金属橡胶弹性元件的动力学建模,提出一种新的建模方法,用此方法建立了基于迟滞回线拟和分解的高次弹性复合阻尼模型。该模型用非线性刚度和非线性复合阻尼机理构造,模型中的参数由试验数据辨识。用所建模型重构恢复力-位移迟滞回线,结果表明该模型能很好描述这类非线性振动系统的特性。     

基于模糊逻辑的舰船维修经费预测

针对多输入、单输出的复杂非线性系统，基于Ｔａｋａｇｉ－Ｓｕｇｅｎｏ　模糊规则给出了一种系统预测模型，分别用模糊Ｃ－均值聚类算法和线性回归方法导出模型参数．利用该模型对舰船维修经费进行了预测，并进行了精度分析．     

A probabilistic evaluation of helicopter lift capability

This paper describes a technique for the calculation of the probability that a helicopter can lift a specified load, or number of loads with a specified frequency distribution, in a given geographical region. This probability is computed by determining the bivariate altitude-temperature probability distribution for the specified region. The payload capability at any given temperature and altitude is calculated from standard performance equations. By integrating this over the altitude-temperature distribution, it is possible to obtain the probability distribution of payload capability, from which the required probabilities of lifting specific loads can be determined.     

Optimal replacement of military aircraft: an economic approach

A nonlinear optimization model is developed in this paper to identify the optimal replacement strategy for military aircraft. In the model, the aircraft operating and maintenance (O&M) costs per available year are estimated as a function of age during the aircraft life cycle. After determining the optimal replacement policy, the model is applied to the CF Long-Range Patrol CP-140A Arcturus fleet. A sensitivity analysis is also carried out to assess the impact of some key model parameters on the result.     

Sample sizes for β-expectation tolerance limits which control both tails of the normal distribution

Sample sizes for tolerance limits are given on a normal distribution. β-Expectation tolerance intervals are defined and constructed to control the proportion in each tail of the normal distribution. We also require with a high probability that the proportion in each tail is close to its corresponding expected coverage. Under these conditions. we dctcrniine a minimum sample size and its accompanying tolerance limits. Graphs of minimum sample sizes for the tolerance limits are provided. The computation for minimum samplc sizes is based on the bivariate noncentral t distribution. Examples are given to illustrate the use of the graphs.     

模型递推辨识算法及应用

研究了具有线性参数的非线性多项式模型的数据阵L－D分解性质,其中D是对角阵,L是带有单位元素的下三角阵．结果表明,通过因子L可以估计出模型的参数,通过因子D可以选择模型中的项;提出了同时进行模型的结构确定和参数估计的递推辨识算法．该算法可用于船舶运动的实时建模．实际应用结果表明,该算法可以有效地辨识多项式等线性参数的非线性模型．     

考虑非线性退化与随机失效阈值的剩余寿命预测

针对广泛存在的非线性退化设备,现有方法尚未考虑随机失效阈值对剩余寿命预测结果的影响。因此,通过对设备性能退化过程进行分析,提出了一种综合考虑非线性退化与随机失效阈值的剩余寿命预测方法。基于Wiener过程构建了考虑个体差异与测量误差的非线性退化模型;基于卡尔曼滤波算法建立状态空间模型以实现对退化状态的在线更新;基于极大似然法估计失效阈值分布系数估计方法,得到随机失效阈值的概率分布;基于随机失效阈值推导出剩余寿命的概率分布,实现对剩余寿命的在线预测。算例研究表明,所提方法可以有效地提升剩余寿命预测的准确性,具备一定工程应用价值。     

有限声速的纯方位算法

针对纯方位条件下对等速直航目标观测的算法问题,将目标运动要素及平均声速作为待估计参数,给出了计算非线性最小二乘法目标函数梯度与Hessian矩阵的解析公式,基于这些公式,可以构造估计目标运动要素的一些算法及编程实现。部分数值实验表明,信赖域算法、Levenberg-Marquardt算法与Matlab用于解非线性最小二乘问题的函数lsqnonlin的计算精度基本一致。     

Nonlinear integer programming for various forms of constraints

A theoretical and computational investigation is made of the performance of a dynamic-programming-based algorithm for nonlinear integer problems with various types of constraints. We include linear constraints, aggregated linear constraints, separable nonlinear constraints and constraints involving maxima and minima. Separability of the objective function is assumed. The new feature of the algorithm is that two types of fathoming or pruning are used to reduce the size of tables and number of computations: fathoming by bounds and fathoming by infeasibility.