双参数指数分布的可靠寿命的广义置信下限

基于双参数指数分布定数截尾数据,利用Weerahanandi给出的广义置信区间的概念,建立了可靠寿命的广义置信下限,并从理论上证明了我们给出的广义置信下限是精确的,即基于广义置信下限的区间估计的覆盖率等于要求的置信水平.广义置信下限需要通过数值方法得到,但是计算方法是简单直接的.在小样本情形下,通过对基于广义置信下限的置信区间与Engelhardt-Bain近似置信区间覆盖率的模拟比较,发现广义置信下限更令人满意.     

双参数指数分布型元件并联系统的可靠性的广义置信下限

本文对于两个独立双参数指数分布元件组成的并联系统,基于两个元件的定数截尾数据,利用Weerahandi给出的广义枢轴量和广义置信区间的概念,建立了可靠性的广义置信下限,并从理论上研究了广义置信下限的频率性质.广义置信下限可以通过数值方法得到,计算方法是简单直接的.在小样本情形下,通过与Bootstrap置信下限的模拟研究,发现广义置信下限的覆盖率更令人满意.     

左截尾双参数指数分布的可靠寿命的广义置信下限

本文基于左截尾双参数指数分布定数截尾数据,利用Weerahandi给出的广义枢轴量和广义置信区间的概念,通过两种不同的方法建立了可靠寿命的广义置信下限.第1种方法利用位置参数无限制时可靠寿命的广义置信下限来定义左截尾情形下可靠寿命的限制广义置信下限,第2种方法基于广义枢轴量在限制参数空间上的条件分布给出可靠寿命的条件广义置信下限.我们分别研究了这两种置信下限的性质,给出了简单易行的数值计算方法.模拟比较表明限制广义置信下限具有好的覆盖率性质,条件广义置信下限的覆盖率与参数取值有关,但它有时比限制广义置信下限具有更大均值和更小标准差.     

两参数Weibull分布平均寿命的置信下限

王蓉华，徐晓岭．两参数Ｗｅｉｂｕｌ分布平均寿命的置信下限．数理统计与管理，１９９８，１７（２），４３～４５．本文给出了求两参数Ｗｅｉｂｕｌ分布定数截尾下平均寿命置信下限的一种方法     

K型区间删失数据下参数的置信限

基于K型区间删失数据,利用样本空间排序法给出参数优良的置信下限和计算置信下限的递推公式.     

两参数威布尔分布可靠度和可靠寿命的精确置信限

本文讨论两参数威布尔分布可靠度和可靠寿命的置信限。对于小样本的情况比较了可靠度的MLE和基于极值分布参数的BLIE,BLUE所得的可靠度的点估计和置信下限的优劣。给出了求可靠度置信下限的用表。     

求参数函数置信限的一般性WCF方法及其应用

该文将求参数函数置信下限的WCF方法推广到参数的估计量之间具有相关性的一般情形; 利用推广了的公式, 给出了求单个威布尔型设备及含威布尔型设备的系统可靠度置信下限的方法, 并进行了模拟研究. 模拟结果表明, 该方法优于基于渐近正态性的近似方法, 尤其是在中小样本情况.     

多个独立同分布应力作用下的极值型——极值型（Ⅰ—Ⅲ）模式的结构可靠性估计

本文讨论了在多个独立同分布应力作用下的极值型－极值型（Ⅰ－Ⅲ）模式结构可靠性估计，给出了分布参数及结构可靠度ｐｒ＝Ｐ（ｍａｘ（Ｓｉ）〈Ｒ）的矩估计，极大似然估计及置信下限。     

基于分布矩拟合的小子样二项分布参数P的置信下限

基于分布矩拟合的原则,给出小子样二项分布成功率P的置信下限的一种计算方法,通过与经典置信下限及reformualtion方法计算的置信下限进行比较,得出分布矩拟合方法计算的置信下限是合理和可信的.     

拉格朗日函数在确定参数置信区间时的应用

1 问题的提出 参数的区间估计就是根据估计量的分布，在一定的可靠度下，指出被估计的总体参数所在的可能数值范围．其具体做法是：对于来自总体的样本（X1，X2，…，Xn），找两个统计量^θ（X1，X2，…，Xn）和^θ2（X1，X2，…，Xn），使 P（^θ1〈θ〈^θ2）=1-α 区间（^θ1，^θ2）称为θ的置信区间，^θ2和^θ1分别称为置信区间的上、下限．1-α称为置信系数，也称为置信概率或置信度．而α是事先给定的一个小正数，它是指参数估计不准的概率。     

串联系统可靠性虚拟系统法置信下限的小样本性质

本文讨论了具有r个成败型元件串联系统可靠性的置信下限问题。研究了虚拟系统法置信下限的小样本性质,证明了,在通常情况下虚拟系统法置信下限要大于常见的L-M法置信下限.更一般地,本文证明了在成败型试验中,当成功数与试验数之比保持不变时,试验次数的增加将直接缩小成功率置信区间的长度。     

Minimax confidence bound of the normal mean under an asymmetric loss function

This paper considers a minimax confidence bound of the normal mean under an asymmetric loss function. A minimax confidence bound is obtained for the case that the variance is known or unknown. The admissibility of the minimax confidence bound is also considered for the case of known variance.     

The exact extreme response and the confidence extreme response analysis of structures subjected to uncertain-but-bounded excitations

In this study, the methods for computing the exact bounds and the confidence bounds of the dynamic response of structures subjected to uncertain-but-bounded excitations are discussed. Here the Euclidean norm of the nodal displacement is considered as the measurement of the structural response. The problem of calculating the exact lower bound, the confidence (outer) approximation and the inner approximation of the exact upper bound, and the exact upper bound of the dynamic response are modeled as three convex QB (quadratic programming with box constraints) problems and a problem of quadratic programming with bivalent constraints at each time point, respectively. Accordingly, the DCA (difference of convex functions algorithm) and the vertex method are adopted to solve the above convex QB problems and the quadratic programming problem with bivalent constraints, respectively. Based on the inner approximation and the outer approximation of the exact upper bound, the error between the confidence upper bound and the exact upper bound of dynamic response could be yielded. Specially, we also investigate how to obtain the confidence bound of the dynamic response of structures subjected to harmonic excitations with uncertain-but-bounded excitation frequencies. Four examples are given to show the efficiency and accuracy of the proposed method.     

Nonparametric statistical analysis of an upper bound of the ruin probability under large claims

In this paper, the classical Poisson risk model is considered. The claims are supposed to be modeled by heavy-tailed distributions, so that the moment generating function does not exist. The attention is focused on the probability of ruin. We first provide a nonparametric estimator of an upper bound of the ruin probability by Willmot and Lin. Then, its asymptotic behavior is studied. Asymptotic confidence intervals are studied, as well as bootstrap confidence intervals. Results for possibly unstable models are also obtained.     

A stopping rule for symbolic dynamic filtering

One of the key issues in symbolic dynamic filtering (SDF) is how to obtain a lower bound on the length of symbol blocks for computing the state probability vectors of probabilistic finite-state automata (PFSA). Having specified an absolute error bound at a confidence level, this short work formulates a stopping rule by making use of Markov chain Monte Carlo (MCMC) computations.     

Predicting a cyclic Poisson process

We construct and investigate a (1−α)-upper prediction bound for a future observation of a cyclic Poisson process using past data. A normal based confidence interval for our upper prediction bound is established. A comparison of the new prediction bound with a simpler nonparametric prediction bound is also given.     

Consensus formation of two-level opinion dynamics

Opinion dynamics have received significant attention in recent years. This paper proposes a bounded confidence opinion model for a group of agents with two different confidence levels. Each agent in the population is endowed with a confidence interval around her opinion with radius αd or (1-α)d, where α ∈ (0,1/2] represents the differentiation of confidence levels. We analytically derived the critical confidence bound d_c = 1/(4α) for the two-level opinion dynamics on ?. A single opinion cluster is formed with probability 1 above this critical value regardless of the ratio p of agents with high/low confidence. Extensive numerical simulations are performed to illustrate our theoretical results. Noticed is a clear impact of p on the collective behavior: more agents with high confidence lead to harder agreement. It is also experimentally revealed that the sharpness of the threshold d_c increases with α but does not depend on p.     

Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution

Chen and Bhattacharyya (1988,Comm. Statist. Theory Methods,17, 1857–1870) derived the exact distribution of the maximum likelihood estimator of the mean of an exponential distribution and an exact lower confidence bound for the mean based on a hybrid censored sample. In this paper, an alternative simple form for the distribution is obtained and is shown to be equivalent to that of Chen and Bhattacharyya (1988). Noting that this scheme, which would guarantee the experiment to terminate by a fixed timeT, may result in few failures, we propose a new hybrid censoring scheme which guarantees at least a fixed number of failures in a life testing experiment. The exact distribution of the MLE as well as an exact lower confidence bound for the mean is also obtained for this case. Finally, three examples are presented to illustrate all the results developed here.     

随机设计下非参数回归模型变点的小波检测与估计

A wavelet method of detection and estimation of change points in nonparametric regression models under random design is proposed. The confidence bound of our test is derived by using the test statistics based on empirical wavelet coefficients as obtained by wavelet transformation of the data which is observed with noise. Moreover, the consistence of the test is proved while the rate of convergence is given. The method turns out to be effective after being tested on simulated examples and applied to IBM stock market data.