Estimation of a smooth quantile function under the proportional hazards model

The problem of estimating a smooth quantile function, Q(·), at a fixed point p, 0 < p < 1, is treated under a nonparametric smoothness condition on Q. The asymptotic relative deficiency of the sample quantile based on the maximum likelihood estimate of the survival function under the proportional hazards model with respect to kernel type estimators of the quantile is evaluated. The comparison is based on the mean square errors of the estimators. It is shown that the relative deficiency tends to infinity as the sample size, n, tends to infinity.     

Economic design of an attribute control chart for monitoring mean life based on multiple deferred state sampling

In this paper, we design an attribute np control chart using multiple deferred state (MDS) sampling under Weibull distribution based on time truncated life test. This chart is constructed for monitoring the variation of mean life of the product in a manufacturing process. The optimal parameters of MDS sampling and the control limit coefficients are determined so that the in‐control average run length (ARL) is as close as to the target ARL. The optimal parameters of MDS sampling are sample size and number of successive subgroups required for declaring the current state of process. Out‐of‐control ARL is considered as a measure of the performance of proposed chart and reported with determined optimal parameters for various shift constants. The out‐of‐control ARL of the proposed chart obtained under various distributions is compared with each other. The performance of proposed control chart is compared with the performance of the existing control chart designed under single sampling. In addition, the economic design of proposed chart using variable sampling interval scheme is discussed, and sensitivity analysis on expected costs is also investigated.     

Applications of a multi-state risk factor/mortality model in life insurance

Mortality rates are known to depend on socio-economic and behavioral risk factors, and actuarial calculations for life insurance policies usually reflect this. It is typically assumed, however, that these risk factors are observed only at policy issue, and the impact of changes that occur later is not considered. In this paper, we present a discrete-time, multi-state model for risk factor changes and mortality. It allows one to more accurately describe mortality dynamics and quantify variability in mortality. This model is extended to reflect health status and then used to analyze the impact of selective lapsation of life insurance policies and to predict mortality under reentry term insurance.     

基于MATLAB的交通事故发生规律的模糊分布拟合

借助于数学软件MATLAB,运用模糊数学方法,探讨中国交通事故发生及危害的变化规律.首先,作中国交通事故统计数据的散点图,观察发现交通事故的变化同时具有线性增长总趋势和波动性特征,呈现出复杂的非线性组合特点;再对这些数据进行归一化处理,给出交通事故的模糊隶属函数;最后对交通数据进行分布拟合、组合回归处理,得到交通事故非线性模糊分布函数.结果表明,随着时间的变化,中国交通事故的死亡人数呈线性与正态叠加波动上升趋势,受伤人数呈线性与正弦叠加波动上升趋势,发生起数与损失折款都呈双峰正态分布波动趋势,2002年以来交通状况正在好转.得到的结果能客观地反映交通事故的现状分布和精确地刻划中国交通事故发生及危害变化规律,对于交通事故预测、综合治理具有重要的理论意义和应用价值,可供交通事故研究和有关部门制定交通安全管理决策作参考.     

Estimation of the number of failures in the Weibull model using the ordinary differential equation

In estimating the number of failures using right truncated grouped data, we often encounter cases that the estimate is smaller than the true one when we use the likelihood principle to conditional probability. In infectious disease spread predictions, the SIR model described by simultaneous ordinary differential equations is commonly used, and it can predict reasonably well the number of infected patients even when the size of observed data is small. We have investigated whether the ordinary differential equation model can estimate the number of failures more accurately than does the likelihood principle under the condition of right truncated grouped data. The positive results are obtained in the Weibull model, similarly to the cases of the SARS, A(H1N1), and FMD.     

基于时隙ALOHA协议的数据传输二人随机博弈模型

在一个给定的拓扑网络中研究关于数据传输的二人随机博弈模型.两个局中人（源节点）试图通过一个公共节点向目的节点传输随机数据包,这些数据包被分为重要的数据包和不重要的数据包两类,假设每个局中人都有一个用于存储数据包的有限容量的缓冲器.通过构造数据传输的成本分摊和奖励体系,把这种动态的冲突控制过程建模为具有有限状态集合的随机博弈,研究局中人在这种随机博弈模型下的非合作以及合作行为.在非合作情形下,给出纳什均衡的求解算法;在合作情形下,选择Shapley值作为局中人支付总和的分配方案,并讨论其子博弈一致性,提出使得Shapley值为子博弈一致的分配补偿程序.     

Influence of induced magnetic field on peristaltic flow in an annulus

This paper looks at the influence of the induced magnetic field on peristaltic transport through a uniform infinite annulus filled with an incompressible viscous and Newtonian fluid. The present theoretical model may be considered as mathematical representation to the movement of conductive physiological fluids in the presence of the endoscope tube (or catheter tube). The inner tube is uniform, rigid, while the outer tube has a sinusoidal wave traveling down its wall. The flow analysis has been developed for low Reynolds number and long wave length approximation. Exact solutions have been established for the axial velocity, stream function, axial induced magnetic field, current distribution and the magnetic force function. The effects of pertinent parameters on the pressure rise and frictional forces on the inner and outer tubes are investigated by means of numerical integrations, also we study the effect of these parameters on the pressure gradient, axial induced magnetic field and current distribution. The phenomena of trapping is further discussed.     

On an estimate of the size of the exceptional set in the lemma on the logarithmic derivative

In the paper, an exact estimate of the size of the exceptional set in the lemma on the logarithmic derivative is obtained. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 603–607, April, 2000.     

On the existence of minimum contrast estimates in binary response model

When random samples are drawn from a 3-parameter distribution with a shifted origin and the observations corresponding to each sample are binary, criteria for the existence of minimum contrast estimates are given. These criteria can be drived by a method, called the probability contents boundary analysis. The probabilities of the existence of maximum likelihood estimates and least squares estimates are evaluated, by simulation with 1000 replications, in the case where the underlying distribution is a 3-parameter lognormal distribution or a 3-parameter loglogistic distribution.     

The elixir of life: using a maintenance, repair and replacement model based on virtual and operating age in the water industry

Processing equipment in the water industry is subject to decayand requires maintenance, repair and eventual replacement. Thechallenge of competition within the water industry and the accompanyingregulatory regime requires that actions be integrated and costeffective. This is an industry, which has considerable dataon the failure of its equipment, but until recently very fewmodels of the maintenance process have been built. This paper describes the context of this problem for cleanwater processing where the equipment is that required to purifywater. It proposes a model based on the virtual and operatingage of the components. The operating age reflects the true ageof the equipment while the virtual age allows for the cumulativeeffect of maintenance actions performed on the equipment. Themodel also allows for different types of equipment by describingdegradation by Cox's proportional hazards model. Thus the specialfeatures of the equipment and environment in which the equipmentoperates are described by a set of characteristics, which modifythe hazard rate of the failure time of the equipment. This approachusing Cox's model with virtual and operating age can be appliedto other processing industries including the gas industry andthe ‘dirty water’ side of the water industry. The model is formulated as a stochastic dynamic programmingor Markov decision process and the form of the optimal policyis determined. This shows that repair and replacement shouldonly be performed when the equipment has failed and describesgeneral conditions when replacement is appropriate. The optimalpolicy is calculated numerically using the value iteration algorithmfor a specific example based on data on failure.     

机制转换条件下股市收益率跳跃行为研究:基于RS-ARJI模型的以中国股市为例的实证分析

为检验股市收益率机制转换特性,考察机制转换条件下股市收益率的跳跃特征,以及在不同机制下跳跃行为对股市收益率的冲击效应,将Markov机制转换思想引入自回归跳跃(ARJI)模型,构建一个机制转换自回归跳跃(RS-ARM)模型.基于该模型对中国股市进行实证研究,结果表明:股市存在高、低波动两种机制,高波动时期的跳跃幅度和强度及其对股市收益率的冲击均大于低波动时期.同时,波动率估计和预测评价指标显示,RS-ARJI模型优于目前被广泛使用的GARCH模型和ARJI模型.