Estimation under modified Weibull distribution based on right censored generalized order statistics

In this paper, the maximum likelihood (ML) and Bayes, by using Markov chain Monte Carlo (MCMC), methods are considered to estimate the parameters of three-parameter modified Weibull distribution (MWD(β, τ, λ)) based on a right censored sample of generalized order statistics (gos). Simulation experiments are conducted to demonstrate the efficiency of the proposed methods. Some comparisons are carried out between the ML and Bayes methods by computing the mean squared errors (MSEs), Akaike's information criteria (AIC) and Bayesian information criteria (BIC) of the estimates to illustrate the paper. Three real data sets from Weibull(α, β) distribution are introduced and analyzed using the MWD(β, τ, λ) and also using the Weibull(α, β) distribution. A comparison is carried out between the mentioned models based on the corresponding Kolmogorov–Smirnov (K–S) test statistic, {AIC and BIC} to emphasize that the MWD(β, τ, λ) fits the data better than the other distribution. All parameters are estimated based on type-II censored sample, censored upper record values and progressively type-II censored sample which are generated from the real data sets.     

Estimating the propagation rate of a viral infection of potato plants via mixtures of regressions

A problem arising from the study of the spread of a viral infection among potato plants by aphids appears to involve a mixture of two linear regressions on a single predictor variable. The plant scientists studying the problem were particularly interested in obtaining a 95% confidence upper bound for the infection rate. We discuss briefly the procedure for fitting mixtures of regression models by means of maximum likelihood, effected via the EM algorithm. We give general expressions for the implementation of the M-step and then address the issue of conducting statistical inference in this context. A technique due to T. A. Louis may be used to estimate the covariance matrix of the parameter estimates by calculating the observed Fisher information matrix. We develop general expressions for the entries of this information matrix. Having the complete covariance matrix permits the calculation of confidence and prediction bands for the fitted model. We also investigate the testing of hypotheses concerning the number of components in the mixture via parametric and 'semiparametric' bootstrapping. Finally, we develop a method of producing diagnostic plots of the residuals from a mixture of linear regressions.     

Degeneracy in the Maximum Likelihood Estimation of Univariate Gaussian Mixtures for Grouped Data and Behaviour of the EM Algorithm

Abstract.  In the context of the univariate Gaussian mixture with grouped data, it is shown that the global maximum of the likelihood may correspond to a situation where a Dirac lies in any non-empty interval. Existence of a domain of attraction near such a maximizer is discussed and we establish that the expectation-maximization (EM) iterates move extremely slowly inside this domain. These theoretical results are illustrated both by some Monte-Carlo experiments and by a real data set. To help practitioners identify and discard these potentially dangerous degenerate maximizers, a specific stopping rule for EM is proposed.     

Online coupon consumption problem

Nowadays, it is popular that the dealer makes profits by selling a kind of discount coupons, which can be used as money to purchase commodities with total cost less than or equal to the face value of the coupon. We can purchase a coupon at a price of 0<s≤1 times its face value and the number of potential purchasable coupons is a given integer l. The customer has the option to buy the goods by cash completely or by a discount coupon. However, each piece of goods can only use one coupon and the coupon used must have enough balance for the goods. The objective is to minimize the total cost for purchasing all the goods. In this paper, we reduce the problem to a special bin packing model. We consider the online problems for all 0<s≤1 and 1≤l≤∞. We present optimal online algorithms for all 0<s≤1 when l=∞ and l=1. For 2≤l<∞, we give both a lower bound and an algorithm, and show the algorithm is optimal for l=2. A preliminary version of this paper appeared in the proceedings of the 1st International Symposium on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies, Lecture Notes in Computer Science. Y. Jiang supported by Natural Science Foundation of Zhejiang Province (Y605316). Z. Tan supported by Natural Science Foundation of China (10671177, 60021201).     

模拟电路故障诊断的神经网络方法

提出了一种采用改进的ＢＰ快速算法实现模拟电路软故障诊断的方法。文中对构造神经网络交流故障字典的过程给出了详细说明，特别是隐层节点数确定，测试信号频率的优选及ＭＡＴＬＡＢ神经网络工具箱的使用。实例表明，人工神经网络技术可应用于有容差模拟电路的故障诊断。     

图像艺术的发展对绘画的影响

以计算机和网络为核心的信息技术，影响到人类生活的诸多方面，也给绘画艺术教育带来了巨大的机遇和挑战。从图象和绘画艺术的历史沿革和现状入手，分析论述图象艺术的发展对绘画的影响。     

Identifiable finite mixtures of location models for clustering mixed-mode data

For clustering mixed categorical and continuous data, Lawrence and Krzanowski (1996) proposed a finite mixture model in which component densities conform to the location model. In the graphical models literature the location model is known as the homogeneous Conditional Gaussian model. In this paper it is shown that their model is not identifiable without imposing additional restrictions. Specifically, for g groups and m locations, (g!)m–1 distinct sets of parameter values (not including permutations of the group mixing parameters) produce the same likelihood function. Excessive shrinkage of parameter estimates in a simulation experiment reported by Lawrence and Krzanowski (1996) is shown to be an artifact of the model's non-identifiability. Identifiable finite mixture models can be obtained by imposing restrictions on the conditional means of the continuous variables. These new identified models are assessed in simulation experiments. The conditional mean structure of the continuous variables in the restricted location mixture models is similar to that in the underlying variable mixture models proposed by Everitt (1988), but the restricted location mixture models are more computationally tractable.     

The robust economic statistical design of the Hotelling's T2 chart

ABSTRACT

Economic statistical designs aim at minimizing the cost of process monitoring when a specific scenario or a set of estimated process and cost parameters is given. But, in practice the process may be affected by more than one scenario which may lead to severe cost penalties if the wrong design is used. Here, we investigate the robust economic statistical design (RESD) of the T² chart in an attempt to reduce these cost penalties when there are multiple scenarios. Our method is to employ the genetic algorithm (GA) optimization method to minimize the total expected monitoring cost across all distinct scenarios. We illustrate the effectiveness of the method using two numerical examples. Simulation studies indicate that robust economic statistical designs should be encouraged in practice.     

Kullback-leibler information approach to the optimum measurement point for bayesian estimation

When an appropriate parametric model and a prior distribution of its parameters are given to describe clinical time courses of a dynamic biological process, Bayesian approaches allow us to estimate the entire profiles from a few or even a single observation per subject. The goodness of the estimation depends on the measurement points at which the observations were made. The number of measurement points per subject is generally limited to one or two. The limited measurement points have to be selected carefully. This paper proposes an approach to the selection of the optimum measurement point for Bayesian estimations of clinical time courses. The selection is made among given candidates, based on the goodness of estimation evaluated by the Kullback-Leibler information. This information measures the discrepancy of an estimated time course from the true one specified by a given appropriate model. The proposed approach is applied to a pharmacokinetic analysis, which is a typical clinical example where the selection is required. The results of the present study strongly suggest that the proposed approach is applicable to pharmacokinetic data and has a wide range of clinical applications.     

一种新的GPS导航卫星选择算法

针对利用全球定位系统（GPS）进行定位导航时对实时性的要求，提出了一种新的导航卫星选择算法。该算法比传统算法的计算量小得多。仿真结果表明，该算法所得出的结果与传统算法很接近，能满足导航定位的实时性精度要求。