Yang Zhenlin
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Publication On the failure rate estimation of the inverse Gaussian distribution(2001) Yang, Z.; Lee, R.T.C.; STATISTICS & APPLIED PROBABILITYNew estimators of the inverse Gaussian failure rate are proposed based on the maximum likelihood predictive densities derived by Yang (1999). These estimators are compared, via Monte Carlo simulation, with the usual maximum likelihood estimators of the failure rate and found to be superior in terms of bias and mean squared error. Sensitivity of the estimators against the departure from the inverse Gaussian distribution is studied.Publication Transformation approaches for the construction of Weibull prediction interval(2003-07-28) Yang, Z.; See, S.P.; Xie, M.; INDUSTRIAL & SYSTEMS ENGINEERING; STATISTICS & APPLIED PROBABILITYTwo methods of transforming the Weibull data to near normality, namely the Box-Cox method and Kullback-Leibler (KL) information method, are discussed and contrasted. A simple prediction interval (PI) based on the better KL information method is proposed. The asymptotic property of this interval is established. Its small sample behavior is investigated using Monte Carlo simulation. Simulation results show that this simple interval is close to the existing complicated PI where the percentage points of the reference distribution have to be either simulated or approximated. The proposed interval can also be easily adjusted to have the correct asymptotic coverage. © 2002 Elsevier Science B.V. All rights reserved.Publication Predictive densities for the lognormal distribution and their applications(1999) Yang, Z.; STATISTICS & APPLIED PROBABILITYMaximum likelihood predictive densities (MLPDs) for a future lognormal observation are obtained and their applications to reliability and life testing are considered. When applied to reliability and failure rate estimations, they give estimators that can be much less biased and less variable than the usual maximum likelihood estimations (MLEs) obtained by replacing the unknown parameters in the density function by their MLEs. When applied to lifetime predictions, they give prediction intervals that are shorter than the usual frequentist intervals. Using the MLPDs, it is also rather convenient to construct the shortest prediction intervals. Extensive simulations are performed for comparisons. A numerical example is given for illustration. © 2000 Elsevier Science Ltd. All rights reserved.Publication Predicting a Future Median Life through a Power Transformation(2001) Yang, Z.; STATISTICS & APPLIED PROBABILITYA simple and unified prediction interval (PI) for the median of a future lifetime can be obtained through a power transformation. This interval usually possesses the correct coverage, at least asymptotically, when the transformation is known. However, when the transformation is unknown and is estimated from the data, a correction is required. A simple correction factor is derived based on large sample theory. Simulation shows that the unified PI after correction performs well. When compared with the existing frequentist PI's, it shows an equivalent or a better performance in terms of coverage probability and average length of the interval. Its nonparametric aspect and the ease of usage make it very attractive to practitioners. Real data examples are provided for illustration.Publication An investigation of transformation-based prediction interval for the Weibull median life(2002) Yang, Z.; See, S.P.; Xie, M.; INDUSTRIAL & SYSTEMS ENGINEERING; STATISTICS & APPLIED PROBABILITYStatistical inference based on the Weibull distribution, a distribution widely used in reliability and survival analysis, is usually difficult as it often involves numerical computation and approximation. However, this distribution can be transformed to near-normality by a simple power transformation. Based on this transformation, a prediction interval (PI) for its median can be easily constructed through an inverse transformation. The procedure for selecting the best power transformation through minimizing Kullback-Leibler information is described. The property of this transformation-based PI is investigated. Simple correction factors are also proposed. It is shown that the transformation-based PI with corrections performs well, irrespective of the sample size and parameter values. Simulation results show that the new PI generally outperforms the existing PI. Numerical examples are given for illustration.Publication A new statistic for regression transformation(2000-06) Yang, Z.; STATISTICS & APPLIED PROBABILITYA new statistic for testing a regression transformation is proposed based on a result of Yang (1999). This statistic is shown to be stable, having a null distribution almost independent of model type and parameter values, accurate and easy to implement. The statistic is of the Wald-type and thus is compared with the Wald statistic given by Lawrance (1987) in terms of size, null distribution and power using simulation. The simulation results show that the new statistic generally outperforms that of Lawrance.Publication Some asymptotic results on Box-Cox transformation methodology(1996) Yang, Z.; ECONOMICS & STATISTICSPublication A comparison of likelihood and Bayesian inference for the threshold parameter in the inverse Gaussian distribution(1998) Desmond, A.F.; Yang, Z.; STATISTICS & APPLIED PROBABILITYLikelihood and Bayesian inferences for the threshold parameter of the three parameter inverse Gaussian distribution are compared and contrasted. When there is no prior information available and sample size is moderate, theoretical and empirical results suggest advantages to the Bayesian approach. Use of the conjugate prior can favorably affect the Bayesian inference in a substantial way. Copyright © 1998 by Marcel Dekker, Inc.Publication On robustness of usual confidence region under transformation misspecification(1998) Yang, Z.; STATISTICS & APPLIED PROBABILITYRobustness of confidence region for linear model parameters following a misspecified transformation of dependent variable is studied. It is shown that when error standard deviation is moderate to large the usual confidence region is robust against transformation misspecification. When error standard deviation is small the usual confidence region could be very conservative for structured models and slightly liberal for unstructured models. However, the conservativeness in structured case can be controlled if the transformation is selected with the help of data rather than prior information since this is the case when data is able to provide a very accurate estimate of transformation.Publication Maximum likelihood predictive densities for the inverse Gaussian distribution with applications to reliability and lifetime predictions(1999-09) Yang, Z.; STATISTICS & APPLIED PROBABILITYMaximum likelihood predictive densities (MLPD) for the inverse Gaussian distribution are derived for the cases of one or both parameters unknown. They are then applied to obtain estimators of the reliability function and prediction or shortest prediction intervals for a future observation. Comparisons with the existing likelihood or frequentist methods show that the MLPD estimators of reliability gives smaller bias and smaller MSE for a wide range of population values, and that the MLPD prediction intervals are shorter while preserving the correct coverage probability. The shortest MLPD prediction intervals further sharpen the above equitailed MLPD intervals in terms of interval lengths.