指数分布冷贮备系统产品的统计分析——转换开关指数型的情形

给出了全样本场合下指数分布冷贮备系统产品寿命分布中参数θ≠λ时的矩估计和极大似然估计,通过Monte-Carlo给出了参数矩估计的精度,考察了1000次满足条件时所需要的模拟次数,随着样本量的增大,矩估计存在的比率逐渐增大,而极大似然估计的结果与样本有关.同时给出了参数θ=λ时的矩估计、极大似然估计和逆矩估计,通过Monte-Carlo模拟考察了参数点估计精度,认为矩估计比较优.文章还给出了求参数区间估计的两种方法——精确方法和近似方法,通过Monte-Carlo模拟认为精确方法精度较高.     

Cox-Ingersoll-Ross模型的统计推断

本文研究了Cox—Ingersoll—Ross模型的统计推断问题.给出了CIR过程的平稳均值m与平稳方差v的矩估计,并利用m和v给出了CIR过程中尺度参数α与波动率β之间的关系,讨论了参数α的条件矩估计和渐近极大似然估计.并通过数值模拟对条件矩估计,渐近极大似然估计这两种方法作了比较.     

逐步增加Ⅱ型截尾下Pareto分布的Bayes估计

基于逐步增加的Ⅱ型截尾样本,当Pareto分布的尺度参数已知时,分别在平方损失和LINEX损失下讨论了其形状参数和可靠性指标(失效率和可靠度)的Bayes估计,并用Monte-Carlo方法对估计结果的MSE,进行了模拟比较.结果表明了在LINEX损失下的估计结果更有效.     

Burr Type Ⅻ分布的统计推断

该文讨论了两参数Burr Type Ⅻ分布基于逐次定数截尾样本的参数估计,导出了有关参数的点估计和区间估计.我们利用模拟方法对所给点估计和参数的最大似然估计作了比较,模拟结果显示所给点估计优于常用的最大似然估计.最后,用一个实际例子说明本文所给方法.     

Burr Type XII 分布的统计推断

该文讨论了两参数 Burr Type XII 分布基于逐次定数截尾样本的参数估计, 导出了有关参数的点估计和区间估计. 我们利用模拟方法对所给点估计和参数的最大似然估计作了比较, 模拟结果显示所给点估计优于常用的最大似然估计. 最后, 用一个实际例子说明本文所给方法.     

Copula函数中参数的矩估计方法

Copula函数是将多维随机变量的联合分布和其边缘分布连接起来的一种函数.关于Copula函数的理论和应用已有不同深度的研究,特别是Copula函数中未知参数的估计问题.本文研究了Gumbel Copula函数的参数估计,提出了矩估计和近似矩估计两种方法,分别得到了未知参数的估计结果,并通过模拟研究对这两种方法进行了比较,结果显示矩估计方法更为合理.     

双参数指数分布环境因子的Bayes估计

讨论了定数截尾样本下双参数指数分布环境因子的极大似然估计、区间估计和Bayes估计.以参数后验密度的商密度作为环境因子的后验密度,并结合专家经验运用Bayes方法给出了环境因子在平方损失下和LINEX损失下的Bayes估计.最后运用Monte Carlo方法对各估计结果的均方误差(MSE),进行了模拟比较.结果表明LINEX损失下环境因子的估计较好.     

基于离散观测的OU型过程的经验似然估计

基于离散观测样本,借助条件特征函数,提出了OU型过程参数的经验似然估计,并证明了最大经验似然估计的相合性和渐近正态性,同时证明了在适当的附加条件下,该估计是渐近有效的.当驱动Lévy过程具有某种特殊形式时,发现OU型过程的强度参数能够首先估计出来.在此特殊情形下,提出了OU型过程中其余参数的最大经验似然估计,并讨论了其相合性、渐近正态性和渐近有效性.基于经验似然比统计量,给出了参数检验和估计方程检验的似然比检验方法.模拟显示所提出的估计方法是准确和稳定的.     

广义指数分布下恒定应力加速寿命试验的贝叶斯分析

研究产品寿命服从广义指数分布的有关加速寿命试验的贝叶斯统计分析.首先介绍了广义指数分布在恒定应力下的加速寿命试验基本过程;其次在完全样本,和定数截尾样本下,分别给出了广义指数分布参数的贝叶斯估计;最后运用随机模拟方法对各种估计结果的优良性进行了分析比较.     

嵌套模拟组合风险度量的方差减小

嵌套模拟是金融中非常复杂的问题,涉及的计算量很大.试图用方差减小技术来减小嵌套模拟估计的方差,进而减小均方误差,以减少计算成本,提高模拟效率.对要用嵌套模拟估计的风险度量,提出了对外层随机因子的双参数重要性抽样方法,以及对外层随机因子的单参数重要性抽样方法与控制变量方法结合的方法.数值实验表明,双参数重要性抽样法和单参数重要性抽样方法与控制变量方法结合的方法效果都比普通的单参数重要性抽样方法好.     

The collective reserving model

This paper sets out a model for analysing claims development data, which we call the collective reserving model (CRM). The model is defined on the individual claim level and it produces separate IBNR and RBNS reserve estimators at the collective level without using any approximations. The CRM is based on ideas from a paper by Verrall, Nielsen and Jessen (VNJ) from 2010 in which a model is proposed that relies on a claim giving rise to a single payment. This is generalised by the CRM to the case of multiple payments per claim. All predictors of outstanding claims payments for the VNJ model are shown to hold for this new model. Moreover, the quasi-Poisson GLM estimation framework will be applicable as well, but without using an approximation. Furthermore, analytical expressions for the variance of the total outstanding claims payments are given, with a subdivision on IBNR and RBNS claims. To quantify the effect of allowing only one payment per claim, the model is related and compared to the VNJ model, in particular by looking at variance inequalities. The double chain ladder (DCL) method is discussed as an estimation method for this new model and it is shown that both the GLM- and DCL-based estimators are consistent in terms of an exposure measure. Lastly, both of these methods are shown to asymptotically reproduce the regular chain ladder reserve estimator when restricting predictions to the lower right triangle without the tail, motivating the chain ladder technique as a large-exposure approximation of this model.     

Prediction error in the chain ladder method

We define a chain ladder model which allows for the study of three different error types: (a) diversifiable process error, (b) non-diversifiable process error, and (c) parameter estimation error. The model is based on the classical stochastic chain ladder model introduced by Mack [Mack, T., 1993. Distribution-free calculation of the standard error of chain ladder reserve estimates. Astin Bull. 23(2), 213-225]. In order to clearly distinguish the different sources of prediction uncertainty, we have to slightly modify that classical chain ladder model.     

Addendum to ‘The multi-year non-life insurance risk in the additive reserving model’ [Insurance Math. Econom. 52(3) (2013) 590–598]: Quantification of multi-year non-life insurance risk in chain ladder reserving models

This is the first study to derive closed-form analytical expressions for multi-year non-life insurance risk in the chain ladder model. Extending on previous research on the additive reserving model, we define multi-year risk via prediction errors of multi-year claims development results including both observed and future accident years. A resampling argument and a first-order Taylor approximation address the quantification of estimation errors and multiplicative dependencies in the chain ladder framework, respectively. From our generalized multi-year approach, we deduce estimators for reserve and premium risks in multi-year view and their implicit correlation. We reproduce well-known results from literature for the special cases of one-year and ultimo view. Further, we comment on how to obtain estimators for generalized versions of the chain ladder method. A case study demonstrates the applicability of our analytical formulae.     

Robust loss reserving in a log-linear model

It is well known that the presence of outlier events can overestimate or underestimate the overall reserve when using the chain-ladder method. The lack of robustness of loss reserving estimators leads to the development of this paper. The appearance of outlier events (including large claims—catastrophic events) can offset the result of the ordinary chain ladder technique and perturb the reserving estimation. Our proposal is to apply robust statistical procedures to the loss reserving estimation, which are insensitive to the occurrence of outlier events in the data. This paper considers robust log-linear and ANOVA models to the analysis of loss reserving by using different type of robust estimators, such as LAD-estimators, M-estimators, LMS-estimators, LTS-estimators, MM-estimators (with initial S-estimate) and Adaptive-estimators. Comparisons of these estimators are also presented, with application of a well known data set.     

Chain recurrence rates and topological entropy

We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the well-known notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of chain transitive maps. These notions of recurrence are defined using ε-chains, and the minimal lengths of these ε-chains give a way to measure recurrence time (chain recurrence and chain mixing times). We give upper and lower bounds for these recurrence times and relate the chain mixing time to topological entropy.     

低碳环境下供应链差异化定价与协调机制研究

以低碳和普通产品两个制造商和一个零售商组成的两级供应链系统为研究对象,探讨了供应链的差异化定价与协调机制问题。求解得到了两制造商和零售商的最优定价策略及可行的低碳产品生产成本范围。研究发现:1)分散决策的差异化定价策略无法达到供应链协调;2)在可行的低碳产品生产成本范围内,低碳产品制造商、零售商和整个供应链系统的利润都随低碳产品生产成本的增加而减少,只有普通产品制造商的利润随低碳产品生产成本的增加而增加。因此,降低低碳产品生产成本是促进低碳产品推广的关键。针对分散决策造成供应链效率损失的情况,采用Shapley值法进行协调,并给出了契约协调机制。最后,通过算例分析了消费者价格敏感性变化和低碳产品生产成本上升对最优决策和供应链利润的影响。     

A Scoring Criterion For Learning Chain Graphs

A chain graph allows both directed and undirected edges, and contains the underlying mathematical properties of the two. An important method of learning graphical models is to use scoring criteria to measure how well the graph structures fit the data. In this paper, we present a scoring criterion for learning chain graphs based on the Kullback Leibler distance. It is score equivalent, that is, equivalent chain graphs obtain the same score, so it can be used to perform model selection and model averaging.     

Chain of BBGKY equations for bimolecular chemical reactions

A dynamically verified statistical theory of moderately dense gases developed by Bogoliubov and others is generalized to the case of bimolecular chemical reactions in a gas. The corresponding chain of BBGKY equations is derived. From this chain, the kinetic equations for one-molecule distribution functions are obtained in the approximation of bimolecular and trimolecular interactions. Deceased. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 2, pp. 163–178, May, 1997.     

供应链网络可靠性的多层Bayes估计模型

对供应链网络可靠性进行界定和分析,以节点企业间的协同为基础,得到可靠度计算模型,以此为依据采集实证样本无失效运行的数据.根据供应链网络可靠性统计特性,建立一种多层Bayes估计方法,应用于样本可靠性评估中.在估计失效率的基础上,对供应链网络可靠度进行估计,对仿真结果进行分析,显示多层Bayes估计方法应用效果较好,精确度高,反映了参数不确定性对供应链网络可靠性的影响,能够较好地解决依据无失效数据判定供应链网络可靠性水平的问题.     

A simulation based approach to the parameter estimation for the three-parameter gamma distribution

The gamma distribution is one of the commonly used statistical distribution in reliability. While maximum likelihood has traditionally been the main method for estimation of gamma parameters, Hirose has proposed a continuation method to parameter estimation for the three-parameter gamma distribution. In this paper, we propose to apply Markov chain Monte Carlo techniques to carry out a Bayesian estimation procedure using Hirose’s simulated data as well as two real data sets. The method is indeed flexible and inference for any quantity of interest is readily available.