基于径向基函数的分数年龄假设

人寿保险中的生命表通常只给出生存函数在整数年龄上的分布情况.当需要对非整数年龄上的生存函数进行计算时就必须做适当的分数年龄假设(FAA).传统的FAA有简单易计算的优点,但它们却无法保证能精确地捕捉到生存函数的真实趋势,并且会导致死力函数不符合常理.FAA本质上是对整数年龄数据进行插值.径向基函数(RBF)模型作为一种有效的插值技术被广泛地应用于计算机试验设计与分析中.文章将其引入到寿险精算理论中,对生存函数进行插值,并用成功拟合的生存函数构建死力函数及平均余命函数.RBF模型的有效性通过了Makeham函数来进行验证,实验表明,RBF模型的插值能力远远高于经典的FAA模型.     

统计检验中假设的设置方法

统计假设检验作为一种统计推断方法,必须先建立科学的假设。文章讨论了假设的建立方法,认为应当先把研究者希望得到的结论设置为备择假设,再把相反的结论作为原假设,但等号必须置于原假设中。如果样本数据提供的信息足以支持单侧检验,那么左侧检验和右侧检验的结论是相同的。反之,则应当进行双侧检验。可靠的单侧检验结论应当以拒绝原假设的双侧检验结论为前提。     

分数布朗运动下B-S权证定价模型的修正

分析证券市场的有效性,指出其线性范式与现实市场状况并不符合。传统的金融学认为证券收益率服从对数正态分布,而大量的实证表明收益率分布与正态分布相比有＂尖峰胖尾＂特征,具有分形结构。在此基础上剖析了传统B-S权证定价模型的不足,结合分形市场中的分数布朗运动,提出了基于分形理论的B-S股本权证定价模型,考虑了股本稀释效应。由于股本权证定价模型需要已知企业股权价值及其波动率,但企业价值是权证价格的函数。基于此,运用数值方法以股票价格和波动率来估计企业价值波动率,并给出了在实际运用中的案例。     

一致性分数阶优化灰色模型及其应用

传统的分数阶灰色预测模型在时间序列预测中具有较好的适应性和预测的有效性,但其累加和差分计算式比较复杂。一致性分数阶累加相对于一般的分数阶累加,形式更简单,更便于计算和理论推导。为了提高模型的适应性和预测能力,文章在CFGM(1,1)白化方程中引入一个新的可变系数,扩大了原有白化方程的适用范围,并在此基础上构建了一致性分数阶优化灰色模型,即CFOGM(1,1)模型。最优一致性分数阶阶数和可变系数通过PSO算法最小化平均相对误差获得。将构建的模型运用到两个实例中并与其他经典的灰色预测模型进行对比,结果表明所提出的模型具有较高的拟合和预测精度。     

CAPM的检验方法及假设条件研究

资本资产定价模型是第一个关于金融资产定价的均衡模型,它对确定金融资产的基本价值提供了依据,对分析和抑制资产泡沫的形成无疑具有重要的意义.依据国外学者对CAPM的研究成果,对CAPM的统计检验方法和假设条件进行系统探讨,旨在为CAPM在中国证券市场的合理应用提供理论支持.     

分数维非线性协整及误差校正模型

本文在分数维和非线性的框架下讨论了经济系统中的长期均衡关系,提出了分数维非线性协整的概念及对应的误差校正模型,基于小波神经网络给出了分数维非线性协整的检验及其误差校正模型的建模方法。实证研究发现中国股市存在分数维非线性协整关系,据此建立了相应的分数维非线性误差校正模型.该模型的预测效果优于带有外生变量的非线性自回归移动平均模型。     

数字地价模型的构建方法及参数选择

基于地统计内插构建数字地价模型是目前国内研究地价空间分布的常用手段.既往的研究大多侧重空间变异分析或不同模型结果的比较,较少探讨一个完整的建模过程及过程中一些重要参数如何科学选择与设置.文章以2008-2014年石家庄市主城区土地交易数据为例,借助ArcGIS、GS+软件平台,深入探讨了基于地统计学原理,利用Kriging插值的方法,构建数字地价模型的完整过程,并重点探究此建模过程中获取最优参数的方法.结果表明:基于地统计方法构建的数字地价模型,能够合理地模拟区域地价空间分布形态;并通过探索性空间数据分析、变异函数分析、不同模型拟合优度对比、交叉验证精度检验等手段,有效地保证了建模参数的科学性和准确性.     

“全面二孩”政策下的中国人口结构解析

文章编制了连续年份的动态完全生命表,采用变参数年龄移算法模型,对我国2016--2040年的人口进行了精准评估,结果显示:我国将在2025年迎来人口峰值14.05亿,在2040年左右迈入“超少子化”和“超级老龄化”的行列,老龄化的发展速度将超过少子化,男女比例失衡的现状会得到改观.可见,“全面二孩”政策对人口问题全方位调整的短期效应并不明显,但会改善人口性别结构和家庭内部结构.     

全球价值链下中国增加值贸易的效应研究——基于广义假设抽取法的分析

利用世界投入产出表相关数据,构建了多区域假设抽取模型,实证分析了全球价值链下中国增加值贸易的效应。研究发现:(1)中国与其他国家的贸易往来有助于提升自身对各行业的增加值消费,也有助于其他国家之间的增加值贸易以及其他国家的增加值消费,在全球价值链下中国的增加值贸易发挥了重要作用。(2)中国与其他国家贸易往来对不同的国家影响不一样,对美国、日本的增加值进出口影响较大。(3)全球价值链下中国的各行业增加值贸易的效应大小并不一致,部分行业的作用大于其他行业,例如农、林、牧、渔业的内部效应大于其他行业。根据以上结果,在全球经济一体化的格局下,中国有必要进一步扩大增加值贸易,其他国家也需要加强与中国的双边贸易,另外,在采取进出口税率调整等政策扩大增加值贸易时需要注意行业的差异。     

拟合索赔数据的一种新方法：叠加分布模型

一、引言保险公司在收取续保费时,要充分利用每一个投保人的索赔历史记录,这些历史记录包括各投保期的索赔次数以及每一次索赔的大小等等。根据这些信息,保险公司利用损失分布模型将这些信息数据拟合出来,然后预测在续保期内投保人将给保险公司带来的损失。在对数据进行拟合以前,保险公司要选择合适的损失模型。就目前而言,拟合索赔大小的模型包括指数分布模型、伽马分布模型、对数正态分布模型、帕累托分布模型等;拟合索赔次数的损失模型有很多,包括泊松分布模型、负二项分布模型、泊松—逆高斯分布模型等。这些模型在拟合数据时都有比较良…     

Fractional Age Assumption Based on Cubic Polynomial Interpolation

This article proposes a new fractional age assumption (FAA) based on the cubic polynomial interpolation (CPI) and applies it to estimate the mortality rate and related actuarial quantities. The validity of the method under CPI is proved theoretically and the valuable advantages of CPI assumption are discussed based on three different perspectives—utilized death information, property of mortality force, and optimality criterion. The results show that CPI assumption has distinct valuable superiority compared with other FAAs in references. Finally under CPI assumption we study the calculations of some important actuarial quantities in life contingencies.     

Discrimination Measures for Fractional Integrated Models Based on Wavelets

Discrimination measures have been well developed for stationary time series. However in a large number of phenomena, long-term dependencies are involved. In this article, we are dealing with discrimination of fractional integrated models. Kullback–Leibler and Chernoff's discrimination measures are approximated, using the discrete wavelet transform (DWT) for discrimination of these time series classes. The simulation study indicates low misclassification rate, related to the approximations of Kullback–Leibler and Chernoff discrimination measures. Application to problem of classifying seismic data showed that our procedure performs as well as other procedures.     

A Numerical Method for Estimating the Variance of Age at Maximum Growth Rate in Growth Models

Studies on maturation and body composition mention age at peak height velocity (PHV) as an important measure that could predict adulthood outcome. The age at PHV is often derived from growth models such as the triple logistic fitted to the stature (height) data. Theoretically, for a well-behaved growth function, age at PHV could be obtained by setting the second derivative of the growth function to zero and solving for age. Such a solution obviously depends on the parameters of the growth function. Therefore, the uncertainty in the estimation of age at PHV resulting from the uncertainty in the estimation of the growth model, need to be accounted for in the models in which it is used as a predictor. Explicit expressions for the age at PHV and, consequently the variance of the estimate of the age at PHV, do not exist for some of the commonly used nonlinear growth functions, such as the triple logistic function. Once an estimate of this variance is obtained, it could be incorporated in subsequent modeling either through measurement error models or by using the inverse variances as weights. A numerical method for estimating the variance is implemented. The accuracy of this method is demonstrated through comparisons in models where explicit solution for the variance exists. The method of estimating the variance is illustrated by applying to growth data from the Fels study and subsequently used as weights in modeling two adulthood outcomes from the same study.     

A New Goodness-of-Fit Test Based on the Laplace Statistic for a Large Class of NHPP Models

ABSTRACT

Nonhomogeneous Poisson processes (NHPP) provide many models for hardware and software reliability analysis. In order to get an appropriate NHPP model, goodness-of-Fit (GOF for short) tests have to be carried out. For the power-law processes, lots of GOF tests have been developed. For other NHPP models, only the Conditional Probability Integral Transformation (CPIT) test has been proposed. However, the CPIT test is less powerful and cannot be applied to some NHPP models. This article proposes a general GOF test based on the Laplace statistic for a large class of NHPP models with intensity functions of the form αλ(t, β). The simulation results show that this test is more powerful than CPIT test.     

基于重复购买理论的一种新的客户选择方法

在今天越来越激烈的市场竞争之中,越来越多的公司已经从产品驱动的市场竞争策略转向客户驱动的市场竞争策略。并且随着计算机技术及数据挖掘方法的飞速发展,直接市场营销越来越受到重视。如何选择目标客户邮寄货单的问题也就越来越引起市场直销者的兴趣。计分模型及增益表选择方法和单群预测及选择方法是目前普遍采用的两种客户选择方法。在平稳市场的假设下,客户的购买模式服从著名的重复购买理论。基于这个理论,本文提出了一种新的客户选择方法,即两群预测及选择方法。应用实际的客户数据比较这三种不同的方法,结果表明新方法表现最好。     

A New Robust Regression Method Based on Particle Swarm Optimization

Regression analysis is one of methods widely used in prediction problems. Although there are many methods used for parameter estimation in regression analysis, ordinary least squares (OLS) technique is the most commonly used one among them. However, this technique is highly sensitive to outlier observation. Therefore, in literature, robust techniques are suggested when data set includes outlier observation. Besides, in prediction a problem, using the techniques that reduce the effectiveness of outlier and using the median as a target function rather than an error mean will be more successful in modeling these kinds of data. In this study, a new parameter estimation method using the median of absolute rate obtained by division of the difference between observation values and predicted values by the observation value and based on particle swarm optimization was proposed. The performance of the proposed method was evaluated with a simulation study by comparing it with OLS and some other robust methods in the literature.     

A New Fatigue Life Model Based on the Family of Skew-Elliptical Distributions

ABSTRACT

Fatigue is structural damage produced by cyclic stress and tension. An important statistical model for fatigue life is the Birnbaum–Saunders distribution, which was developed to model ruptured lifetimes of metals that had been subjected to fatigue. This model has been previously generalized and in this article we extend it starting from a skew-elliptical distribution, the incorporation of the elliptical aspect makes the kurtosis flexible, and the skewness makes the asymmetry flexible. In this work we found the probability density, reliability, and hazard functions; as well as its moments and variation, skewness, and kurtosis coefficients. In addition, some properties of this new distribution were found.     

一种免疫否定分段匹配选择的数据分类方法

根据免疫否定选择原理,设计了基于掩码分段匹配的否定选择分类器,克服连续r位匹配法的缺陷。给出了适用于免疫优化的分类规则编码及分类信息分的评价。通过免疫进化对其进行群体优化以约简数据规则集。避免了传统分类算法缺乏全局优化能力的缺点,提高了对样本的识别能力。实验结果表明本文方法提高了数据分类的准确性,在数据分类准确率及平均信息分上优于传统的分类方法。     

A Nonparametric Shewhart-Type Signed-Rank Control Chart Based on Runs

Measures of distributional symmetry based on quantiles, L-moments, and trimmed L-moments are briefly reviewed, and (asymptotic) sampling properties of commonly used estimators considered. Standard errors are estimated using both analytical and computer-intensive methods. Simulation is used to assess results when sampling from some known distributions; bootstrapping is used on sample data to estimate standard errors, construct confidence intervals, and test a hypothesis of distributional symmetry. Symmetry measures based on 2- or 3-trimmed L-moments have some advantages over other measures in terms of their existence. Their estimators are generally well behaved, even in relatively small samples.     

A New GWMA Control Chart for Monitoring Process Mean and Variability

In this article, we extend a single exponentially weighted moving average semicircle (EWMA-SC) chart to a single generally weighted moving average (GWMA) chart. This new control chart can effectively combine the features of the SC chart with GWMA techniques, and can easily indicate the source and direction of a change. We perform simulations to evaluate the average run length, standard deviation of the run length, and diagnostic abilities of the GWMA-SC and EWMA-SC charts. An extensive comparison shows that the GWMA-SC control chart is more sensitive than the EWMA-SC chart for detecting small shifts in the process mean and/or variability.