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.     

一个新的具有单调降失效率的寿命分布

本文由Pareto分布和Logarithmic分布"混合"生成两参数具有单调降失效率的新型寿命分布,研究了该分布的矩、熵、失效率函数、平均剩余寿命和参数的极大似然估计,应用EM算法求参数的极大似然估计,进行了数值模拟.     

排序集抽样下指数分布产品的寿命性能评估

为了提高指数分布产品的寿命性能评估效率,研究了排序集抽样下寿命性能指数的极大似然估计,证明了其具有存在性和唯一性.针对似然方程没有显式解的问题,采用部分期望法给出具有显式表达式的修正极大似然估计,并利用排序集样本构造出寿命性能指数的置信区间.仿真结果表明:不仅排序集抽样下修正极大似然估计的效率一致高于简单随机抽样下极大...     

一类加权可靠指数分布

本文研究了一种含有形状参数和尺度参数的加权可靠性指数分布.利用变量替换以及极大似然法,研究了在特定尺度参数下此分布的构造性表示,并导出了计算该分布两个参数极大似然估计的迭代解,同时还给出了估计参数的渐近分布形式.     

Pareto-Geometric分布

本文提出了一种具有单调失效率的新型寿命分布, 即由Pareto分布和Geometric分布生成的两参数的Pareto-Geometric分布, 研究了该分布的各种性质和参数极大似然估计的存在唯一性, 并应用 EM 算法得到了参数的极大似然估计值和相应的渐近方差、协方差.     

非正则位置参数模型中的拟极大似然估计

当分布密度的形式未知时，参数的极大似然估计没有明确的解析表达式，也不能通过设计算法由计算机运算得到。本文我们将从该分布中抽取的样本当作是来自另一个形式已知的分布密度的样本，该已知分布密度的选取依赖于未知的分布密度，但是具有与未知分布相似的边界性质。基于这两个分布族，我们提出了拟极大似然估计的概念，同时，对这种拟极大似然估计的渐近性质进行了讨论。结果表明拟极大拟然估计与极大似然估计有关相同的渐近性质，并且由于拟极大似然估计的获得不依赖于未知分布密度的形式，只与一已知的分布密度有关，使得通过计算机可以实现对其的求解。     

Lomax分布极大似然估计的两点研究

本文研究了Lomax分布参数极大似然估计的存在性和估计量的收敛性问题.利用严格的分析法和中心极限定理,获得了Lomax分布极大似然估计的存在性和估计量的渐近正态分布的结果,进一步推广到了有缺失数据的两个Lomax总体中,参数的极大似然估计有强相合性和渐近正态性.     

动态极值排序集抽样设计下Rayleigh分布的参数估计

在统计推断里,参数估计的好坏很大程度上依赖于抽样设计,所以有效的抽样设计将是一项重要的研究课题.本文分别在简单随机抽样(SRS)和动态极值排序集抽样(MERSS)下研究了Rayleigh分布中参数的无偏估计,最优线性无偏估计(BLUE),极大似然估计(MLE)和修正MLE.数值结果显示MERSS估计比SRS估计更有效.     

Logistic回归模型的经验似然诊断

经验似然方法已经被广泛用于许多模型的统计推断.基于经验似然对Logistic回归模型进行统计诊断.首先给出模型的估计方程,进而得到模型参数的极大经验似然估计;其次,基于经验似然研究了三种不同的影响曲率;最后通过实例分析,说明了统计诊断方法的有效性.     

基于经验似然的部分线性模型的统计诊断

经验似然方法己经被广泛应用于许多模型的统计推断.本文基于经验似然对部分线性模型进行统计诊断.首先给出模型的估计方程,进而得到模型参数的极大经验似然估计;其次,基于经验似然研究了三种不同的影响曲率;最后通过随机模拟和实例分析,说明了统计诊断方法的有效性.     

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??In this paper, we concern with the estimation problem for the Pareto distribution based on progressive Type-II interval censoring with random removals. We discuss the maximum likelihood estimation of the model parameters. Then, we show the consistency and asymptotic normality of maximum likelihood estimators based on progressive Type-II interval censored sample.     

基于左截断右删失数据的单参数Pareto分布参数估计

基于EM算法及极大似然法研究了左截断右删失数据下单参数Pareto分布的参数估计,导出其迭代式,并应用随机模拟对参数估计式进行了模拟检验,结果表明迭代式能够快速收敛,EM估计值较为精确.     

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.     

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.     

Statistical Inference for the Parameter of Rayleigh Distribution Based on Progressively Typ e-I Interval Censored Sample

In this paper, the estimation of parameters based on a progressively type-I interval censored sample from a Rayleigh distribution is studied. Different methods of estimation are discussed. They include...     

并联压力—强度模型可靠性研究

In this paper,the reliability of a parallel stress-strength model of exponentiated Pareto distribution is discussed.Different point estimations and interval estimations are proposed.The point estimators obtained are maximum likelihood and Bayesian estimators.The interval estimations obtained are approximate,exact,bootstrap-p and bootstrap-t confidence intervals and Bayesian credible interval.Different methods and the corresponding confidence intervals are demonstrated using some simulation studies.     

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In this paper, we investigate a competing risks model based on exponentiated Weibull distribution under Type-I progressively hybrid censoring scheme. To estimate the unknown parameters and reliability function, the maximum likelihood estimators and asymptotic confidence intervals are derived. Since Bayesian posterior density functions cannot be given in closed forms, we adopt Markov chain Monte Carlo method to calculate approximate Bayes estimators and highest posterior density credible intervals. To illustrate the estimation methods, a simulation study is carried out with numerical results. It is concluded that the maximum likelihood estimation and Bayesian estimation can be used for statistical inference in competing risks model under Type-I progressively hybrid censoring scheme.     

Kullback-Leibler Information Consistent Estimation for Censored Data

This paper is intended as an investigation of parametric estimation for the randomly right censored data. In parametric estimation, the Kullback-Leibler information is used as a measure of the divergence of a true distribution generating a data relative to a distribution in an assumed parametric model M. When the data is uncensored, maximum likelihood estimator (MLE) is a consistent estimator of minimizing the Kullback-Leibler information, even if the assumed model M does not contain the true distribution. We call this property minimum Kullback-Leibler information consistency (MKLI-consistency). However, the MLE obtained by maximizing the likelihood function based on the censored data is not MKLI-consistent. As an alternative to the MLE, Oakes (1986, Biometrics, 42, 177–182) proposed an estimator termed approximate maximum likelihood estimator (AMLE) due to its computational advantage and potential for robustness. We show MKLI-consistency and asymptotic normality of the AMLE under the misspecification of the parametric model. In a simulation study, we investigate mean square errors of these two estimators and an estimator which is obtained by treating a jackknife corrected Kaplan-Meier integral as the log-likelihood. On the basis of the simulation results and the asymptotic results, we discuss comparison among these estimators. We also derive information criteria for the MLE and the AMLE under censorship, and which can be used not only for selecting models but also for selecting estimation procedures.     

Tail Index Estimation and an Exponential Regression Model

One of the most important problems involved in the estimation of Pareto indices is the reduction of bias in case the slowly varying part of the Pareto type model disappears at a very slow rate. In other cases, when the bias problem is not so severe, the application of well-known estimators such as the Hill (1975) and the moment estimator (Dekkers et al. (1989)) still asks for an adaptive selection of the sample fraction to be used in such estimation procedures. We show that in both circumstances, solutions can be constructed for the given problems using maximum likelihood estimators based on a regression model for upper order statistics. Via this technique one can also infer about the bias-variance trade-off for a given data set. The behavior of the new maximum likelihood estimator is illustrated through simulation experiments, among others for ARCH processes.