Bayesian approach to parameter estimation of the generalized pareto distribution

Several methods have been used for estimating the parameters of the generalized Pareto distribution (GPD), namely maximum likelihood (ML), the method of moments (MOM) and the probability-weighted moments (PWM). It is known that for these estimators to exist, certain constraints have to be imposed on the range of the shape parameter,k, of the GPD. For instance, PWM and ML estimators only exist fork>−0.5 andk≤1, respectively. Moreover, and particularly for small sample sizes, the most efficient method to apply in any practical situation highly depends on a previous knowledge of the most likely values ofk. This clearly suggests the use of Bayesian techniques as a way of using prior information onk. In the present work, we address the issue of estimating the parameters of the GPD from a Bayesian point of view. The proposed approach is compared via a simulation study with ML, PWM and also with the elemental percentile method (EPM) which was developed by Castillo and Hadi (1997). The estimation procedure is then applied to two real data sets.     

基于广义高斯噪声模型的低频线谱检测

研究浅海环境噪声中低频线谱的检测问题.首先对实测海洋环境噪声的统计特性进行分析,提出了应用广义高斯分布对海洋环境噪声建模方法.在此基础上,针对低频线谱检测问题,推导了广义高斯噪声场中的最大似然检测器和渐近检测器,给出了弱线谱条件下线谱频率的最大似然估计.最后,利用实测数据对三种检测器的线谱检测性能进行了验证,结果表明:...     

COMPARISONS OF OPTIMAL ACCELERATED TEST PLANS FOR ESTIMATING QUANTILES OF LIFETIME DISTRIBUTION AT THE USE CONDITION

Accelerated life tests (ALTs) and accelerated degradation tests (ADTs) are widely used for the reliability assessment of components or materials. In an ALT, failure times of test units are observed while in an ADT the failure-causing performance characteristic is measured. This article develops optimal ALT and ADT plans for estimating the qth Quantile of the lifetime distribution at the use condition, the latter being an extension of Park and Yum. Then, the two test plans are compared in terms of the asymptotic efficiency in estimating the qth quantile and of the robustness to the mis-specifications of failure probabilities. Computational results show that the ADT provides a more precise estimator than the corresponding ALT, especially when the failure probabilities are small. Concerning the robustness of a test plan to the departures of the guessed failure probabilities from their true values, neither plan completely dominates the other.     

Estimation of Parameters of Universal Distribution of Moments of Failure of Products

A method is proposed for estimating the parameters of a mixture of exponential and Weibull distributions for which the accuracy of preliminary estimates obtained by graphical analysis is refined in accordance with the criterion of maximum likelihood. The efficiency of the proposed method is supported by the results of statistical modeling.     

核最小二乘算法检测红外点目标

对于背景呈非线性变化的复杂图像,用背景预测的方法对红外点目标进行检测时,传统的线性最小二乘法(Least Squares,LS)的效果比较差.文章使用核方法(Kernel Methods,KMs)推导了最小二乘法的非线性版本:核最小二乘算法(Kernel Least Squares,KLS);进一步推导出了更适合动态系统时序预测的指数加权形式的核最小二乘算法(Kemel Exponential wleighted Least Squares,KEWLS).提出了一种基于核方法的红外点目标检测算法,先用KEWLS非线性回归算法预测红外图像背景,再通过自适应门限检测残差图像中的目标,非线性函数回归和红外序列图像检测实验表明核方法较大地改进了算法的非线性函数估计与红外背景预测能力.     

基于极大似然估计的多参考点模态参数识别方法

在考虑随机噪声的情况下,实现了一种基于极大似然估计的多参考点频域模态参数识别方法。该方法采用频响函数的右矩阵分式模型,通过噪声的协方差矩阵对误差向量加权,使用离散时间域中基函数改善数值求解性态。模态参数的估计过程分为两步：首先由基于最小二乘估计的polyLSCF算法获取迭代初值,然后通过Gauss-Newton方法对极大似然函数进行迭代优化,得到精度更高的模态参数识别结果。采用GARTEUR仿真算例对所给出的方法进行了验证,结果表明：在高噪声情况下,利用噪声信息的极大似然估计方法能够显著提高模态参数的识别精度,特别是阻尼的识别精度。     

The Constant Shape Parameter Assumption in Weibull Regression

ABSTRACT

The usual assumption in Weibull regression is that the scale parameter is a function of the predictor variables, and the shape parameter is constant. We consider the problem of estimating parameters in the presence of a nonconstant shape parameter and the effect of assuming a constant shape parameter when it really is not constant. We consider both classical and Bayesian methods of estimation. The misspecification of a constant shape parameter can lead to a loss of power for tests regarding the slope parameters. We find that prediction intervals can be inaccurate when the shape parameter is incorrectly assumed to be constant.     

Maximum Likelihood Parameter Estimation for the Quartic Exponential Distribution

The quartic exponential (QE) distribution defined by the probability density function of the type

is examined in detail.

The problem of obtaining maximum likelihood point estimates of the population parameters reduces to that of identifying the α as functions of the population moments μ _r ′, r = 1, 2.3.4.

The invalidity is explained of methods proposed by previous authors to deal with the nonlinear relationships involved, and a new algorithm is developed which overcomes these objections. The new algorithm is applied to practical data, and the resulting distributions fitted to observed frequencies are shown to compare favourably with those obtained by previous Methods.     

竞争失效产品加速寿命试验的非参数统计方法

研究了竞争失效产品恒定应力加速寿命试验（简称恒加试验）的非参数统计方法,给出了恒加试验的矩估计的最小二乘估计,并研究了它们的优良性。     

A common conjugate prior structure for several randomized response models

In this paper we present a common Bayesian approach to four randomized response models, including Warner's (1965) and other modification for it that appeared thereafter in the literature. Suitable truncated beta distributions are used throughout in a common conjugate prior structure to obtain the Bayes estimates for the proportion of a “sensitive” attribute in the population of interest. The results of this common conjugate prior approach are contrasted with those of Winkler and Franklin's (1979), in which non-conjugate priors have been used in the context of Warner's model. The results are illustrated numerically in several cases and exemplified further with data reported in Liu and Chow (1976) concerning incidents of induced abortions.     

A fatigue model with local sensitivity analysis

The goal of this paper is two fold. First, it introduces a general parametric lifetime model for high‐cycle fatigue regime derived from physical, statistical, engineering and dimensional analysis considerations. The proposed model has two threshold parameters and three Weibull distribution parameters. A two‐step procedure is presented to estimate the parameters. In the first step, the two threshold parameters are estimated by minimizing a least squares regression function. In the second step, the parameters are estimated by the maximum likelihood method after pooling together the data from different stress levels. Since parameter estimation should always be accompanied by a sensitivity analysis of the fitted model, the second goal of this paper is to propose a method for sensitivity analysis for fatigue models. We show that the proposed sensitivity analysis methods are general and can be applied to any fatigue or lifetime model, not just to the one proposed here. Although several fatigue models have been proposed in the literature, to our knowledge this is the first attempt to produce methods for sensitivity analysis for fatigue models. The proposed method makes use of the well‐known duality property of mathematical programming, which states that the partial derivatives of the primal objective function with respect to the constraints right hand side parameters are the optimal values of the negative of the dual problem variables. For the parameters or data, for which sensitivities are sought, to appear on the right hand side, they are converted into artificial variables and set to their actual values, thus obtaining the desired constraints. Both the estimation and sensitivity analysis methods are illustrated by two examples, one application using real fatigue data and the other using simulated data. In addition, the sensitivity proposed method is also applied to an alternative fatigue model. Finally, some specific conclusions and recommendations are also given.