混合分组数据下恒加试验的参数估计

本文研究了恒定心力加速寿命试验在获得混合分组数据情况下的参数估计问题.利用EM算法,扶得了参数极大似然估计的迭代式.该结果推广了分组数据场合下一般恒加试验的参数估计.     

基于EM算法隐Markov模型参数估计

描述最大似然参数估计问题,介绍如何用EM算法求解最大似然参数估计.首先给出EM算法的抽象形式,然后介绍EM算法的一个应用:求隐Markov模型中的参数估计.用EM算法推导出隐Markov模型中参数的迭代公式.     

不同缺失率下EM算法的参数估计

缺失数据是林学研究中普遍存在的一种现象,依据极大似然的思想,对林学研究中有缺失数据的线性模型,推导出了基于EM算法参数估计的迭代公式,为考察样地林分质量,以8个杉木固定样地观测资料的真实数据建立模型,通过计算机模拟和有关的数据分析,得到了12种不同缺失率下参数的估计结果,并与完全数据时的参数估计进行了比较。     

数据分组和右截尾情形下混合指数分布的参数估计

混合模型是可靠性工程,金融保险和计量经济学等领域中的一类重要模型。本文利用EM算法考虑了混合指数分布在分组数据和右截尾情形下的参数估计问题,并给出了相应的参数估计公式,最后的数值模拟表明EM算法对我们的模型是有效的。     

多层线性模型参数估计的MCEM算法

应用Monte Carlo EM(MCEM)算法给出了多层线性模型参数估计的新方法,解决了EM算法用于模型时积分计算困难的问题,并通过数值模拟将方法的估计结果与EM算法的进行比较,验证了方法的有效性和可行性.     

定数截尾混合指数分布在恒加应力下的MCEM加速算法

应用Monte Carlo EM加速算法给出了混合指数分布在恒加应力水平下,在定数截尾场合的参数估计问题,并通过模拟试验说明利用Monte Carlo EM加速算法来估计混合指数分布比EM算法更有效,收敛速度更快.     

Ⅰ型逐阶删失数据下基于EM算法的Weibull参数估计

研究了Ⅰ型逐阶删失数据下基于EM算法的Weibull参数估计,模拟产生不同Weibull参数组合和删失计划下的Ⅰ型逐阶删失数据,应用基于,EM算法的极大似然估计方法得到参数的估计值,并与数值方法得到的极大似然估计值进行对比,说明EM算法的估计效果.对73名肾脏移植患者生存数据进行实例分析,验证了基于EM算法的参数估计方法的可行性.     

变环境情形下Weibull分布分组数据的参数估计

本文研究了变环境情形下Weibull分布分组数据可靠性估计的参数估计问题。给出一种基于EM算法的变环境分组数据Weibull分布参数估计方法,所得估计量具有良好的收敛性,模拟结果表明方法的实践可用性。     

左截断右删失数据下离散型寿命失效率变点模型的Bayes参数估计

利用EM算法和MCMC方法得到了左截断右删失数据下离散型寿命失效率变点模型的参数估计.利用筛选法对缺失数据进行填充,对各参数进行Gibbs抽样.随机模拟证实方法可行且参数估计的精度较高.     

基于EM算法的因子分析中隐变量的条件概率密度函数

因子分析是一种重要的多元统计分析技术,可以采用EM算法迭代得到模型的未知参数,其中一个关键的问题就是在已知观测数据和前一次迭代得到的参数估计值的条件下,如何得到隐变量的条件概率密度函数.国内外的有关文献都不加说明地直接给出了这个函数,本文给出了详细的推导过程.     

单参数Pareto分布变点估计研究

研究单参数Pareto分布存在变点时的估计问题,分别利用极大似然估计法和贝叶斯方法对单参数Pareto分布的变点进行估计,并运用Matlab软件进行随机模拟,随机结果表明贝叶斯方法与极大似然估计相比,估计值更接近真值.     

Robust Estimation of the Generalized Pareto Distribution

One approach used for analyzing extremes is to fit the excesses over a high threshold by a generalized Pareto distribution. For the estimation of the shape and scale parameters in the generalized Pareto distribution, under some restrictions on the value of the scale parameter, maximum likelihood, method of moments and probability weighted moments' estimators are available. However, these are not robust estimators. In this paper we implement a robust estimation procedure known as the method of medians (He and Fung, 1999) to estimate the parameters in the generalized Pareto distribution. The asymptotic distribution of our estimator is normal for any value of the shape parameter except –1.     

Pareto严格稳定分布在保险理赔中的应用

本文研究了Pareto严格稳定分布在保险中的应用.利用极大似然估计的方法得到了Pareto严格稳定分布,正态分布和Pareto分布的参数估计.根据信息准则,表明Pareto严格稳定分布能够较好地拟合保险数据.     

Pareto分布参数的经验Bayes检验的收敛速度:NA样本情形

本文讨论了NA(negativeassociation)样本情形Pareto分布参数的经验Bayes(EB)单侧和双侧检验问题.利用概率密度函数的核估计构造了参数的经验Bayes检验函数,在适当的条件下证明了所提出的经验Bayes检验函数的渐近最优(a.o.)性并获得了其收敛速度.     

NA样本下Pareto分布参数的经验Bayes估计

讨论了Pareto分布在平方损失下参数的Bayes估计,采用同分布负相协样本的核估计方法讨论了参数的经验Bayes(EB)估计问题,并计算了给定条件下参数的经验Bayes估计的收敛速度。最后,对我国高收入阶层的财富分布情况进行了实证分析,实证分析表明我国高收入阶层的财富分布是可以用Pareto分布来描述的。     

Comparing extreme models when the sign of the extreme value index is known

In the literature on analyzing extremes, both generalized Pareto distributions and Pareto distributions are employed to infer the tail of a distribution with a known positive extreme value index. Similar studies exist for a known negative extreme value index. Intuitively, one should not employ the generalized Pareto distribution in the case of knowing the sign of the extreme value index. In this work, we show that fitting a generalized Pareto distribution is equivalent to the model in Hall (1982) in the case of a negative extreme value index, in both improving the rate of convergence and including the bias term of the asymptotic results of that reference. When the extreme value index is known to be positive, we show that fitting a generalized Pareto distribution may be preferred in some cases determined by a so-called second-order parameter and the extreme value index itself.     

Control charts for the Pareto distribution

The Pareto distribution plays an important role in various areas of researchIn this paper, the average run length(ARL) unbiased control charts, which monitor the shape and threshold parameters of the Pareto distribution respectively, are proposed when the incontrol parameters are knownThe effects of parameter estimation on the performance of the proposed control charts are also studiedResults show that the control charts with the estimated parameters are not suitable to be used in the known parameter case, thus the ARL-unbiased control charts for the shape and threshold parameters with the desired ARL0, which consider the variability of the parameter estimates, are further developedThe performance of the proposed control charts is investigated in terms of the ARLFinally, an example is given to illustrate the proposed control charts.     

广义Pareto分布的广义有偏概率加权矩估计方法

广义Pareto分布(GPD)是统计分析中一个极为重要的分布,被广泛应用于金融、保险、水文及气象等领域.传统的参数估计方法如极大似然估计、矩估计及概率加权矩估计方法等已被广泛应用,但使用中存在一定的局限性.虽然提出很多改进方法如广义概率加权矩估计、L矩和LH矩法等,但都是研究完全样本的估计问题,而在水文及气象等应用领域常出现截尾样本.本文基于概率加权矩理论,利用截尾样本对三参数GPD提出一种应用范围广且简单易行的参数估计方法,可有效减弱异常值的影响.首先求解出具有较高精度的形状参数的参数估计,其次得出位置参数及尺度参数的参数估计.通过Monte Carlo模拟说明该方法估计精度较高.     

LINEX损失下Paret0分布族参数的经验Bayes估计

在"nex损失函数下,讨论Pareto分布族参数的经验Bayes(EB)估计问题,文中构造了参数的EB估计,在适当的条件下给出了该估计的收敛速度.最后给出满足定理条件的例子.     

Generalized fiducial confidence intervals for extremes

The generalized Pareto distribution is relevant to many situations when modeling extremes of random variables. In particular, peaks over threshold data approximately follow the generalized Pareto distribution. We use a fiducial framework to perform inference on the parameters and the extreme quantiles of the generalized Pareto. This inference technique is demonstrated both when the threshold is a known and unknown parameter. Assuming the threshold is a known parameter resulted in fiducial intervals with good empirical properties and asymptotically correct coverage. Likewise, our simulation results suggest that the fiducial intervals and point estimates compare favorably to the competing methods seen in the literature. The proposed intervals for the extreme quantiles when the threshold is unknown also have good empirical properties regardless of the underlying distribution of the data. Comparisons to a similar Bayesian method suggest that the fiducial intervals have better coverage and are similar in length with fewer assumptions. In addition to simulation results, the proposed method is applied to a data set from the NASDAQ 100. The data set is analyzed using the fiducial approach and its competitors for both cases when the threshold is known and unknown. R code for our procedure can be downloaded at .