位置参数分布族中Fiducial分布与后验分布的关系

本文考虑本质位置参数分布族中,参数的Fiducial分布与后验分布的等同问题．首先讨论了如何给出Fiducial分布,分析结果表明以分布函数形式给出Fiducial分布要比密度函数形式合理,同时,证明了所给的Fiducial分布具有频率性质．然后,研究在参数受到单侧限制时,Fiducial分布与后验分布等同的问题,给出的充要条件是分布族为指数分布族,此时,先验分布是一个广义先验分布,它不能被Lebesgue测度控制．最后,证明了在参数限制在一个有限区间内时,Fiducial分布与任何先验(包括广义先验分布)下的后验分布不等同．     

位置参数分布族中Fiducial分布与后验分布的关系

本文考虑本质位置参数分布族中,参数的Fiducial分布与后验分布的等同问题.首先讨论了如何给出Fiducial分布,分析结果表明以分布函数形式给出Fiducial分布要比密度函数形式合理,同时,证明了所给的Fiducial分布具有频率性质.然后,研究在参数受到单侧限制时,Fiducial分布与后验分布等同的问题,给出的充要条件是分布族为指数分布族,此时,先验分布是一个广义先验分布,它不能被Lebesgue测度控制.最后,证明了在参数限制在一个有限区间内时,Fiducial分布与任何先验(包括广义先验分布)下的后验分布不等同.     

枢轴分布族中的Fiducial推断

研究枢轴分布族下的Fiducial推断, 提出了求参数的Fiducial分布的一般方法, 在这个方法中Fiducial模型起了重要作用. 方法包含了一些其他求Fiducial分布的方法, 特别地, Fisher提出的第1个Fiducial分布可由此方法导出. 对于单调似然比分布族这样的枢轴分布族, Fiducial分布具有一个Neyman-Pearson观点上的频率性质, 对于文中定义的一类正规参数函数, 它的Fiducial分布也具有上述频率性质. Fiducial推断的一些优点在Fiducial分布的4个应用中展示. 给出了许多例子, 其中的一些例子用现有的方法是得不到Fiducial分布的.     

参数受限制时的Fiducial区间及其应用

给出在参数受限制的情形下, 求参数函数Fiducial区间估计的一般方法, 并将之应用于位置(刻度)分布族和方差分量模型. 对于位置(刻度)分布族中位置(刻度)参数及参数的差异, 证明了所得到的Fiducial区间为频率意义下的置信区间. 对于方差分量模型中普遍关心的3个参数函数, 求出了其Fiducial区间, 并从理论分析和模拟计算两方面讨论了它们的频率性质.     

定数截尾试验下两参数Weibull分布尺度参数的最优稳健Bayes估计

以Г-后验期望损失作为标准,研究了定数截尾试验下两参数W e ibu ll分布尺度参数θ的最优稳健Bayes估计问题.假设尺度参数θ的先验分布在分布族Г上变化,形状参数β已知时,在0-1损失下,得到了θ的最优稳健区间估计,在均方损失下得到θ的最优稳健点估计及区间估计;β未知时,得到了θ的最优稳健点估计及区间估计.最后给出了数值例子,说明了方法的有效性.     

一类可修系统贮存模型及其可用度的Fiducial推断

针对工程实际建立了一种可修系统贮存模型,并在该模型下,导出了在任意时刻系统可用度函数的解析表达式;将该模型应用到服从威布尔分布的系统中,基于系统贮存寿命试验的完全样本,利用Fiducial方法给出了系统可用度的点估计和置信下限,并进行了大量模拟计算,结果表明,该方法在中小样本的情况下仍可给出较为精确的估计．     

截断分布族下参数和损失的可容许估计的几点注记

截断分布族下参数和损失的可容许估计的几点注记吴启光，何敏（中国科学院系统科学所，北京１０００８０）国家自然科学基金资助课题．１９９２年６月２０日收到，１９９３年２月１日收到修改稿．一、引言考虑截断分布族，其分布密度函数为其中为参数，参数空间为一区间（...     

一类可修系统贮存可靠性的MML法推断

本文研究了两种可修贮存模型组成串联系统可靠性统计推断的MML法,并与Fiducial方法进行比较．模拟结果表明MML法对威布尔型设备为主的串联系统可用度进行推断时具有优越性．     

威布尔分布场合下步进应力加速寿命试验的统计分析

本文对寿命分布为两参数威布尔分布,加速模型为逆幂律的情况,由定数截尾步进应力加速寿命试验数据获得加速模型中未知参数的点估计和区间估计,进而给出了加速系数的区间估计,并用一个模拟例子说明方法的应用．     

一类可修威布尔型设备可用度的Fiducial推断

本文对于可维修的威布尔型设备考虑一类修如新模型,导出了在该模型下设备在任意时刻的可用度函数;基于设备寿命试验的完全数据,给出了威布尔分布在任意时刻可靠度的Fiducial分布,由此进一步求出可修威布尔型设备可用度的点估计和置信下限。最后进行了模拟运算,模拟结果表明,该方法在小样本情况下能够作出较精确的推断。     

Interval estimation for the mean of lognormal data with excess zeros

This paper considered interval estimations for the mean of lognormal distribution with excess zeros. We proposed two methods for interval estimation based on an approximate generalized pivotal quantity and a fiducial quantity. Simulation results show that the fiducial approach has highly accurate coverage probability and fairly low bias.     

二项分布基于logit变换的近似信仰推断

利用调整的logit 变换后估计量的渐近正态性对二项分布建立了近似的枢轴方程, 并由此得到了二项分布参数的一种近似信仰分布. 对一样本和两样本情形的数值结果表明, 该近似信仰分布导出的区间估计具有比文献中推荐的区间估计更好的小样本频率性质.     

Fiducial inference in the pivotal family of distributions

In this paper a family, called the pivotal family, of distributions is considered. A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is given. The method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.     

THE INTERVAL ESTIMATIONS FOR THE PARAMETERS AND OTHER RELIABILITY CHARACTERS OF A THREE PARAMETER WEIBULL DISTRIBUTION

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基于β分布的区间估计量化方法

区间估计是专家评价中的重要方法.针对区间估计的特点,构建了区间序列分布,分析了区间序列分布的特性和数字特征;结合β分布及其特性,提出了一种基于β分布的区间估计量化方法,着重探讨了用β分布拟合区间序列分布的原理方法;通过案例分析,表明该方法效果较好,并具有较好的普适性.     

Convergence rates of MLE in a partly linear model

This paper considers the estimation for a partly linear model with case 1 interval censored data. We assume that the error distribution belongs to a known family of scale distributions with an unknown scale parameter. The sieve maximum likelihood estimator (MLE) for the model’s parameter is shown to be strongly consistent, and the convergence rate of the estimator is obtained and discussed.     

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 .     

两种估计区间解法的讨论

依据等概率对称区间和等密度对称区间的概念引出两种估计区间求解方法,并通过两种方法推导证明了等密度对称区间即为最短估计区间.然后分别就F分布和χ2分布情形对这两种区间估计方法作以比较.比较发现,在同样条件下,等密度对称区间总比概率对称区间要短,并且随着自由度增加,两种区间趋于重合.     

Fiducial inference on the largest mean of a multivariate normal distribution

Inference on the largest mean of a multivariate normal distribution is a surprisingly difficult and unexplored topic. Difficulties arise when two or more of the means are simultaneously the largest mean. Our proposed solution is based on an extension of R.A. Fisher’s fiducial inference methods termed generalized fiducial inference. We use a model selection technique along with the generalized fiducial distribution to allow for equal largest means and alleviate the overestimation that commonly occurs. Our proposed confidence intervals for the largest mean have asymptotically correct frequentist coverage and simulation results suggest that they possess promising small sample empirical properties. In addition to the theoretical calculations and simulations we also applied this approach to the air quality index of the four largest cities in the northeastern United States (Baltimore, Boston, New York, and Philadelphia).