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Open Journal of Statistics 2017年第6期7卷 956-963页

作者： Ibrahim Sawadogo Leo Odongo Ibrahim Ly Pan African University Institute of Science Technology and Innovation Nairobi Kenya Department of Statistics and Actuarial Science Kenyatta University (KU) Nairobi Kenya Department of Mathematics University of Ouagadougou Ouagadougou Burkina Faso Department of Mathematics University of Potsdam Potsdam Germany

Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of the new probability distribution function are estimated by the maximum likelihood method under progressive type II censored data via expectation maximization algorithm.

关键词： Maximum Likelihood Type II censored Data Exponentiated Generalized Weibull EM-Algorithm

Composite Quantile Regression for Nonparametric Model with Random censored Data

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Open Journal of Statistics 2013年第2期3卷 65-73页

作者： Rong Jiang Weimin Qian Department of Mathematics Tongji University Shanghai China

The composite quantile regression should provide estimation efficiency gain over a single quantile regression. In this paper, we extend composite quantile regression to nonparametric model with random censored data. The asymptotic normality of the proposed estimator is established. The proposed methods are applied to the lung cancer data. Extensive simulations are reported, showing that the proposed method works well in practical settings.

关键词： Kaplan-Meier Estimator censored Data Composite Quantile Regression Kernel Estimator Nonparametric Model

Comparison of the Bayesian Methods on Interval-censored Data for Weibull Distribution

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Open Journal of Statistics 2014年第8期4卷 570-577页

作者： Al Omari Mohammed Ahmed Department of Mathematics Faculty of Arts and Science in Qilwah Al Baha University Baha KSA

This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can’t be used to solve the parameters analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the scale and shape parameters are obtained via Metropolis-Hastings algorithm. Also Lindley’s approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the mean square error (MSE) to determine the best for estimating of the scale and shape parameters.

关键词： Weibull Distribution Bayesian Method Interval censored Metropolis-Hastings Algorithm Lindley’s Approximation

Bayesian Inference and Prediction of Burr Type XII Distribution for Progressive First Failure censored Sampling

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Intelligent Information Management 2011年第5期3卷 175-185页

作者： Ahmed A. Soliman A. H. Abd Ellah N. A. Abou-Elheggag A. A. Modhesh 不详

This paper deals with Bayesian inference and prediction problems of the Burr type XII distribution based on progressive first failure censored data. We consider the Bayesian inference under a squared error loss function. We propose to apply Gibbs sampling procedure to draw Markov Chain Monte Carlo (MCMC) samples, and they have in turn, been used to compute the Bayes estimates with the help of importance sampling technique. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We further consider two sample Bayes prediction to predicting future order statistics and upper record values from Burr type XII distribution based on progressive first failure censored data. The predictive densities are obtained and used to determine prediction intervals for unobserved order statistics and upper record values. A real life data set is used to illustrate the results derived.

关键词： Burr Type XII Distribution Progressive First-Failure censored Sample Bayesian Estimations Gibbs Sampling Markov Chain Monte Carlo Posterior Predictive Density

Estimation of the Unknown Parameters for the Compound Rayleigh Distribution Based on Progressive First-Failure-censored Sampling

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Open Journal of Statistics 2011年第3期1卷 161-171页

作者： Tahani A. Abushal 不详

This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009). We consider the maximum likelihood and Bayesian inference of the unknown parameters of the model, as well as the reliability and hazard rate functions. This was done using the conjugate prior for the shape parameter, and discrete prior for the scale parameter. The Bayes estimators hav been obtained relative to both symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Also, based on this new censoring scheme, approximate confidence intervals for the parameters of CRD are developed. A practical example using real data set was used for illustration. Finally, to assess the performance of the proposed estimators, some numerical results using Monte Carlo simulation study were reported.

关键词： Compound Rayleigh Distribution Progressive First-Failure censored Scheme Bayesian and Non-Bayesian Estimations Approximate Confidence Intervals

Estimation Based on Progressive First-Failure censored Sampling with Binomial Removals

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Intelligent Information Management 2013年第4期5卷 117-125页

作者： Ahmed A. Soliman Ahmed H. Abd Ellah Nasser A. Abou-Elheggag Rashad M. El-Sagheer Faculty of Science Islamic University Madinah Saudi Arabia Mathematics Department Faculty of Science Al-Azhar University Nasr-City Cairo Egypt Mathematics Department Sohag University Sohag Egypt

In this paper, the inference for the Burr-X model under progressively first-failure censoring scheme is discussed. Based on this new censoring were the number of units removed at each failure time has a discrete binomial distribution. The maximum likelihood, Bootstrap and Bayes estimates for the Burr-X distribution are obtained. The Bayes estimators are obtained using both the symmetric and asymmetric loss functions. Approximate confidence interval and highest posterior density interval (HPDI) are discussed. A numerical example is provided to illustrate the proposed estimation methods developed here. The maximum likelihood and the different Bayes estimates are compared via a Monte Carlo simulation study.

关键词： Burr-X Distribution Progressive First-Failure censored Bayesian and Non-Bayesian Estimations Loss Function Bootstrap Random Removals

Nonparametric Demand Forecasting with Right censored Observations

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Journal of Software Engineering and Applications 2009年第4期2卷 259-266页

作者： Bin ZHANG Zhongsheng HUA 不详

In a newsvendor inventory system, demand observations often get right censored when there are lost sales and no backordering. Demands for newsvendor-type products are often forecasted from censored observations. The Kap-lan-Meier product limit estimator is the well-known nonparametric method to deal with censored data, but it is unde-fined beyond the largest observation if it is censored. To address this shortfall, some completion methods are suggested in the literature. In this paper, we propose two hypotheses to investigate estimation bias of the product limit estimator, and provide three modified completion methods based on the proposed hypotheses. The proposed hypotheses are veri-fied and the proposed completion methods are compared with current nonparametric completion methods by simulation studies. Simulation results show that biases of the proposed completion methods are significantly smaller than that of those in the literature.

关键词： Forecasting Demand censored Nonparametric Product Limit Estimator

Statistical Analysis for Constant-stress Partially Accelerated Life Test with Interval censored Data

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Chinese Quarterly Journal of Mathematics 2019年第1期34卷 1-13页

作者： LONG Bing ZHANG Zhong-zhan School of Mathematics and Physics Jingchu University of Technology College of Applied Sciences Beijing University of Technology

In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially accelerated life tests with Lomax distribution based on interval censored samples. The EM algorithm is used to obtain the maximum likelihood estimations(MLEs) and interval estimations for the shape parameter and acceleration *** average relative errors(AREs), mean square errors(MSEs), the confidence intervals for the parameters, and the influence of the sample size are discussed. The results show that the AREs and MSEs of the MLEs decrease with the increase of sample size. Finally, a simulation sample is used to estimate the reliability under different stress levels.

关键词： Interval censored samples Partially accelerated life test Accelerated factor EM algorithm Fisher information matrix

Evaluation of TIGGE Daily Accumulated Precipitation Forecasts over the Qu River Basin, China

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Journal of Meteorological Research 2019年第4期33卷 747-764页

作者： Li LIU Chao GAO Qian ZHU Yue-Ping XU Institute of Hydrology and Water Resources College of Civil Engineering and ArchitectureZhejiang UniversityHangzhou 310058 School of Civil Engineering Southeast UniversityNanjing 210096

Quantitative precipitation forecasts(QPFs)provided by three operational global ensemble prediction systems(EPSs)from the THORPEX(The Observing System Research and Predictability Experiment)Interactive Grand Global Ensemble(TIGGE)archive were evaluated over the Qu River basin,China during the plum rain and typhoon seasons of 2009–*** post-processing methods,the ensemble model output statistics based on censored shifted gamma distribution(CSGD-EMOS)and quantile mapping(QM),were used to reduce bias and to improve the *** results were evaluated by using three incremental precipitation thresholds and multiple verification *** is demonstrated that QPFs from NCEP and ECMWF presented similarly skillful forecasts,although the ECMWF QPFs performed more satisfactorily in the typhoon season and the NCEP QPFs were better in the plum rain *** of the verification metrics showed evident seasonal discriminations,with more satisfactory behavior in the plum rain *** precipitation tended to be overestimated,but heavier precipitation was always *** post-processed QPFs showed a significant improvement from the raw forecasts and the effects of post-processing varied with the lead time,precipitation threshold,and *** was better corrected at longer lead times and higher ***-EMOS was more effective for probabilistic metrics and the root-mean-square *** had a greater effect on removing bias according to bias and categorical metrics,but was unable to warrant *** general,raw forecasts can provide acceptable QPFs eight days in *** post-processing,the useful forecasts can be significantly extended beyond 10 days,showing promising prospects for flood forecasting.

关键词： TIGGE quantitative precipitation forecasts quantile mapping censored shifted gamma distribution

Convergence rates of MLE in a partly linear model

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Science China Mathematics 2002年第11期45卷 1398-1407页

作者：薛宏旗 Department of Mathematics Graduate School Chinese Academy of Sciences Beijing China

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

关键词： partly linear model, case 1 interval censored data, sieve MLE, strong consistency,convergence rate.