共查询到10条相似文献,搜索用时 140 毫秒
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统计模拟在几何概率问题中应用的注解 总被引:1,自引:0,他引:1
设D为R2上的一个紧集, X 为D上的一个随机覆盖过程的统计量. 由于问题复杂, X的均 值、方差、分布函数均没有解析表达式. 统计模拟可以帮助我们找到它们的近似解. 为了在D上做统 计模拟, 需要D的代表点. 产生代表点的不同方法, 会影响统计模拟的结果. 若D不是一个矩形, 如 何选择合适的代表点至关重要. 文献中研究了一个在单位圆上的随机覆盖问题, 提出在单位圆上产生 代表点的四种方法, 并对这四种方法给予评估. 本文考虑两个随机圆的随机覆盖问题, 给出覆盖面积 的理论公式, 使比较四种产生代表点的方法有一个基准. 我们的研究结果和文献中的结论一致, 并发现 其中两种方法使覆盖面积均值的估计有偏, 且有较大的方差, 这是一个新的结果. 本文进一步指出覆 盖面积的分布可由 β 分布来拟合. 相似文献
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In this paper, we consider the problem of estimating the location and scale parameters of the skew normal distribution introduced by Azzalini. For this distribution, the classic maximum likelihood estimators(MLEs) do not take explicit forms. We approximate the likelihood equations and derive explicit estimators of the parameters. The bias and variance of the estimators are investigated and Monte Carlo simulation studies show that the estimators are as efficient as the classic MLEs. We demonstrate that the probability coverages of the pivotal quantities (for location and scale parameters) based on asymptotic normality are unsatisfactory, especially when the sample size is small. The use of unconditional simulated percentage points of these quantities is suggested. Finally, a numerical example is used to illustrate the proposed inference methods. 相似文献
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Alessandra R. Brazzale 《Journal of computational and graphical statistics》2013,22(3):653-661
Abstract Recently developed small-sample asymptotics provide nearly exact inference for parametric statistical models. One approach is via approximate conditional and marginal inference, respectively, in multiparameter exponential families and regression-scale models. Although the theory is well developed, these methods are under-used in practical work. This article presents a set of S-Plus routines for approximate conditional inference in logistic and loglinear regression models. It represents the first step of a project to create a library for small-sample inference which will include methods for some of the most widely used statistical models. Details of how the methods have been implemented are discussed. An example illustrates the code. 相似文献
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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. 相似文献
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Summary In order to construct a higher-order asymptotic theory of statistical inference, it is useful to know the Edgeworth expansions
of the distributions of related statistics. Based on the differential-geometrical method, the Edgeworth expansions are performed
up to the third-order terms for the joint distribution of any efficient estimators and complementary (approximate) ancillary
statistics in the case of curved exponential family. The marginal and conditional distributions are also obtained. The roles
and meanings of geometrical quantities are elucidated by the geometrical interpretation of the Edgeworth expansions. The results
of the present paper provide an indispensable tool for constructing the differential-geometrical theory of statistics. 相似文献
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This paper considers large sample inference for the regression parameter in a partly linear model for right censored data. We introduce an estimated empirical likelihood for the regression parameter and show that its limiting distribution is a mixture of central chi-squared distributions. A Monte Carlo method is proposed to approximate the limiting distribution. This enables one to make empirical likelihood-based inference for the regression parameter. We also develop an adjusted empirical likelihood method which only appeals to standard chi-square tables. Finite sample performance of the proposed methods is illustrated in a simulation study. 相似文献
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We propose a new measure of proximity of samples based on confidence limits for the bulk of a population constructed using order statistics. For this measure of proximity, we compute approximate confidence limits corresponding to a given significance level in the cases where the null hypothesis on the equality of hypothetical distribution functions may or may not be true. We compare this measure of proximity with the Kolmogorov–Smirnov and Wilcoxon statistics for samples from various populations. On the basis of the proposed measure of proximity, we construct a statistical test for testing the hypothesis on the equality of hypothetical distribution functions. 相似文献
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岩土工程中各土层参数的取值是根据现场及室内试验数据,采用经典统计学方法进行确定的,但这往往忽略了先验信息的作用。与经典统计学方法不同的是,Bayes法能从考虑先验分布的角度结合样本分布去推导后验分布,为岩土参数的取值提供一种新的分析方法。岩土工程勘察可视为对总体地层的随机抽样,当抽样完成时,样本分布密度函数是确定的,故Bayes法中的后验分布取决于先验分布,因此推导出两套不同的先验分布:利用先验信息确定先验分布及共轭先验分布。通过对先验及后验分布中超参数的计算,当样本总体符合N(μ,σ2)正态分布时,对所要研究的未知参数μ和σ展开分析,综合对比不同先验分布下后验分布的区间长度,给出岩土参数Bayes推断中最佳后验分布所要选择的先验分布。结果表明:共轭情况下的后验分布总是比无信息情况下的后验区间短,概率密度函数分布更集中,取值更方便。在正态总体情形下,根据未知参数μ和σ的联合后验分布求极值方法,确定样本总体中最大概率均值μmax和方差σmax作为工程设计采用值,为岩土参数取值方法提供了一条新的路径,有较好的工程意义。 相似文献