定时截尾Weibull分布的双参数的矩估计

讨论了在定时截尾情形下,将Weibull分布转化成指数分布数据或均匀分布,利用平均剩余寿命构造样本矩．从而得出参数的矩估计。并通过大量的Monte-Garlo数值模拟试验证实了所给方法的可行性。     

Robust estimators of the 2-parameter gamma distribution

The available estimators for parameters of the gamma distribution are moment estimators, maximum-likelihood estimators, and approximations to the maximum-likelihood estimators. These estimators are not suitable for small samples; however, they are still being used at the present time. The proposed robust estimators for scale and shape parameters are more suitable for small samples. They have RMS (root-mean-square) errors that are considerably smaller than those of the other estimators. In addition, they are easier to calculate, and are therefore appropriate in many applications     

Robust parameter-estimation using the bootstrap method for the2-parameter Weibull distribution

This paper proposes bootstrap robust estimation methods for the Weibull parameters; it applies bootstrap estimators of order statistics to the parametric estimation procedure. Estimates of the Weibull parameters are equivalent to the estimates using the extreme value distribution. Therefore, the bootstrap estimators of order statistics for the parameters of the extreme value distribution are examined. Accuracy and robustness for outliers are examined by Monte Carlo experiments which indicate adequate efficiency of the proposed reliability estimators for data with some outliers     

Bayes estimation of the parameters and reliability function of the3-parameter Weibull distribution

The authors obtain Bayes estimates of the parameters and reliability function of a 3-parameter Weibull distribution and compare posterior standard-deviation estimates with the corresponding asymptotic standard-deviation estimates of their maximum likelihood counterparts. Numerical examples are given     

Comment on: A general linear-regression analysis applied to the3-parameter Weibull distribution

This paper: (1) examines the results of Yong-Ming Li (see ibid., vol.43, p.255-63, 1994) and points out its errors and shortcomings; and (2) proposes a new graphical method for estimating the parameters of a 3-parameter Weibull distribution     

Parameter estimation for the 3-parameter Gamma distribution usingthe continuation method

This paper shows a maximum-likelihood (ML) parameter estimation algorithm for the 3-parameter Gamma distribution. The algorithm, a combination of the continuation method and the extended Gamma distribution model, can find the local ML estimates of the parameters without a careful selection of the starting point in the iterative process. This algorithm is more efficient than previous algorithms, and can find the multiple local ML estimates     

Properties of Moment Estimators For the 3-Parameter Weibull Distribution

This paper gives a method of constructing moment estimators for the shape, scale, and location parameters of the 3-parameter Weibull distribution. These estimators are asymptotically s-normally distributed around the population values; the asymptotic covariance matrix is obtained. The estimators and their estimated covariance matrix can be constructed by using tables in the paper; the covariance matrix can then be used to construct s-confidence regions for the estimators.     

Comparisons of Point Estimation Methods in the 2-parameter Weibull Distribution

The following 3 estimation methods in a Weibull distribution are well-known; Maximum Likelihood Estimation (MLE), Coefficient of Variation (CV), and Weibull Probability Paper (WPP). By simulation we conclude that the WPP method is best.     

Monte Carlo Comparisons of Parameter Estimators of the 2-parameter Weibull Distribution

A Monte Carlo Simulation was carried out in order to compare three different estimators of the 2-parameter Weibull distribution. The estimators were the ML (maximum likelihood) estimators and two other estimator pairs suggested by Bain & Antle. The Bain-Antle estimators are better than the ML estimator for small samples (in that their bias, standard deviation, and rms error are smaller), whereas the ML estimator is superior in large samples.     

Estimators of 2-parameter Weibull distributions from incompletedata with residual lifetimes

It is common for residual lifetimes to be either discarded or treated as if they were right-censored data estimating two-parameter Weibull distributions. The exact maximum likelihood (ML) estimators for dealing with sampled data with residual lifetimes are formulated. Monte Carlo simulation is used to compare the performance of ML estimators for various approaches to the treatment of residual data. Two types of LS (least squares) estimators are also evaluated: LSMR (LS median rank) estimators and LSNPML (LS nonparametric ML) estimators. For ML estimators, the exact method performs better than the approximate ones. Of the two types of LS estimators, the better one is sensitive to the true value of the shape parameter. The exact ML estimation procedure is therefore preferred over the LS procedures even though the former is not always better     

Improved percentile estimation for the two-parameter Weibull distribution

This paper presents an improvement of a technique recently published to estimate the parameters of the two-parameter Weibull distribution. A simple percentile method is used to estimate the two parameters. Computer simulation is employed to compare the proposed method with the maximum likelihood estimation and graphical methods results. A set of frequently-used and newer expressions for estimating the cumulative density are examined. Comparisons are made with both complete and censored data. The primary advantage of the method is its computational simplicity. Results indicate that with respect to Mean Square Error and estimation of the characteristic value with complete data, the percentile method cannot outperform the maximum likelihood method, although differences are minor in many instances. However, with censored data, improvements over the maximum likelihood are observed. When the shape parameter is estimated, the percentile method is quite competitive with that of maximum likelihood for both complete and censored data under a variety of conditions.     

Limited failure-censored life test for the Weibull distribution

When the distribution of lifetimes is 2-parameter exponential, Balasooriya (1995) provided a failure-censored reliability sampling plan to save test time. This paper extends the Balasooriya sampling plan to the Weibull distribution and provides a limited failure-censored reliability sampling plan (LFCR) to do life testing when test facilities are scarce. The s-expected test time of the LFCR is computed, and the optimal stopping rule of LFCR corresponding to the shortest test time is established. The s-confidence intervals for the parameters are generated     

Shrunken estimators of Weibull shape parameter from type-IIcensored samples

A shrunken estimator of the Weibull shape parameter for failure censored samples is suggested. This shrunken estimator is compared with shrunken estimators previously given. Even for sample sizes of five and ten this shrunken estimator, based on failure data censored at only three and four, respectively, can be used with advantage when one has a reasonable guess for the shape parameter. This estimator has higher efficiency and nearness than other estimators     

Estimation in the 2-parameter exponential distribution with priorinformation

This paper proposes a class of estimators for the scale parameter and for the mean of a 2-parameter exponential distribution, which is important in life testing and reliability theory, given a prior estimate of the scale parameter. The class of estimators for the scale parameter is motivated by the work of Jani (1991). These estimators have smaller mean square error than the classical estimators for all values of the location parameter, and for values of the scale parameter in a neighborhood of the prior estimate. Numerical computations indicate that certain of these estimators substantially improve the classical estimators for values of the scale parameter near the prior estimate, especially for small sample sizes     

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type 1 extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.     

Optimum simple ramp-tests for the Weibull distribution and type-Icensoring

An optimum simple ramp test-accelerated life test with two different linearly increasing stresses-is presented for the Weibull distribution under type I censoring. It is assumed that the inverse power law holds between the Weibull scale parameter and the constant stress and that the cumulative exposure model for the effect of changing stress applies. The optimum plan-low stress rate and proportion of test units allocated to low stress mode-is found. It minimizes the asymptotic variance of the maximum likelihood estimator of a stated quantile at design stress. For selected values of the design parameters, these optimum plans are tabulated, and the effect of the preestimates of these parameters are studied     

Robust minimum-distance estimation using the 3-parameter Weibulldistribution

Maximum-likelihood and minimum-distance estimates were compared for the three-parameter Weibull distribution. Six estimation techniques were developed by using combinations of maximum-likelihood and minimum-distance estimation. The minimum-distance estimates were made using both the Anderson-Darling and Cramer-Von Mises goodness-of-fit statistics. The estimators were tested by Monte Carlo simulation. For each set of parameters and sample size, 1000 data sets were generated and evaluated. Five evaluation criteria were calculated; they measured both the precision of estimating the population parameters and the discrepancy between the estimated and population Cdfs. The robustness of the estimation techniques was tested by fitting Weibull Cdfs to data from other distributions. Whether the data were Weibull or generated from other distributions, minimum-distance estimation using the Anderson-Darling goodness-of-fit statistic on the location parameter and maximum likelihood on the shape and scale parameters was the best or close to the best estimation technique     

A simple procedure for Bayesian estimation of the Weibull distribution

Practical use of Bayesian estimation procedures is often associated with difficulties related to elicitation of prior information, and its formalization into the respective prior distribution. The two-parameter Weibull distribution is a particularly difficult case, because it requires a two-dimensional joint prior distribution of the Weibull parameters. The novelty of the procedure suggested here is that the prior information can be presented in the form of the interval assessment of the reliability function (as opposed to that on the Weibull parameters), which is generally easier to obtain. Based on this prior information, the procedure allows constructing the continuous joint prior distribution of Weibull parameters as well as the posterior estimates of the mean and standard deviation of the estimated reliability function (or the CDF) at any given value of the exposure variable. A numeric example is discussed as an illustration. We additionally elaborate on a new parametric form of the prior distribution for the scale parameter of the exponential distribution. This distribution is not a Gamma (as might intuitively be expected); its mode is available in a closed form, and the mean is obtainable through a series approximation.     

On maximum likelihood estimation for the two parameter Weibull distribution

This paper examines recent results presented on maximum likelihood estimation for the two parameter Weibull distribution. In particular, we seek to explain some recently reported values for estimator bias when the data for analysis contains both times to failure and censored times in operation; our discussion centres on the generation of sample data sets. We conclude that, under appropriate conditions, estimators are asymptotically unbiased, with relatively low bias in small to moderate samples. We then present the results of some further experiments which suggest that the previously reported values for estimator bias can be attributed to the method of generating sample data sets in simulation experiments.     

An engineering approach to Bayes estimation for the Weibull distribution

In this paper an engineering approach to Bayes reliability analysis of Weibull failure data collected under a randomly censored sampling is proposed. The posterior distribution of several decision variables, such as the meanlife, the reliability function, the reliable life, and the hazard rate, are derived, when either a prior information on the reliability or a prior information on the hazard rate is available. Point estimates of the selected decision variables are given, by assuming both symmetric and asymmetric loss functions. Finally, numerical examples are presented to illustrate the proposed estimation procedures.