On a Multiple Three-Decision Problem for Comparing Several Treatments with the Best Control

In this article, a multiple three-decision procedure is proposed to classify p (≥2) treatments as better or worse than the best of q (≥2) control treatments in one way layout. Critical constants required for the implementation of the proposed procedure are tabulated for some pre-specified values of probability of no misclassification. Power function of the proposed procedure is defined and a common sample size necessary to guarantee various pre-specified power levels are tabulated under two optimal allocation schemes. Finally the implementation of the proposed methodology is demonstrated through numerical examples based on real life data.     

Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach

In this paper, maximum likelihood and Bayes estimators of the parameters, reliability and hazard functions have been obtained for two-parameter bathtub-shaped lifetime distribution when sample is available from progressive Type-II censoring scheme. The Markov chain Monte Carlo (MCMC) method is used to compute the Bayes estimates of the model parameters. It has been assumed that the parameters have gamma priors and they are independently distributed. Gibbs within the Metropolis–Hasting algorithm has been applied to generate MCMC samples from the posterior density function. Based on the generated samples, the Bayes estimates and highest posterior density credible intervals of the unknown parameters as well as reliability and hazard functions have been computed. The results of Bayes estimators are obtained under both the balanced-squared error loss and balanced linear-exponential (BLINEX) loss. Moreover, based on the asymptotic normality of the maximum likelihood estimators the approximate confidence intervals (CIs) are obtained. In order to construct the asymptotic CI of the reliability and hazard functions, we need to find the variance of them, which are approximated by delta and Bootstrap methods. Two real data sets have been analyzed to demonstrate how the proposed methods can be used in practice.     

人民币与国外主要货币的尾部相依和联动

文章选择1994年1月到2014年11月的人民币、美元、英镑、日元、欧元和港币等六种货币实际有效汇率的月度数据,首先采用AR-GARCH-t过程对收益率进行过滤,然后运用规则藤Copula函数对标准化残差序列进行建模,探讨人民币“第一次汇改”前后六种汇率之间的波动溢出效应,研究汇率之间的尾部相依和联动现象。研究发现：“第一次汇改”前后,人民币与其它五种货币实际有效汇率之间的相依结构发生了变化,且联动中的主导货币也由美元变为以人民币,但仍可用同一类型的规则藤Copula结构来描述;人民币与其它货币之间都存在对称的或非对称的尾部相依,其中人民币与日元之间存在对称的负尾部相依,而与欧元之间则存在负的上尾部相依。“第一次汇改”后,人民币与美元实际有效汇率之间正的尾部相依程度有所增加,且相依性最大,而港币与美元之间正的尾部相依性有较大幅度的下降。此外,人民币与日元之间负的尾部相依关系也有较大幅度的下降。     

Extended tests for non-zero between-study variance

The ANOVA F-test, James tests and generalized F-test are extended to test hypotheses on the between-study variance for values greater than zero. Using simulations, we compare the performance of extended test procedures with respect to the actual attained type I error rate. Examples are provided to demonstrate the application of the procedures in ANOVA models and meta-analysis.     

Monte Carlo Methods for Bayesian Inference on the Linear Hazard Rate Distribution

The Bayesian estimation and prediction problems for the linear hazard rate distribution under general progressively Type-II censored samples are considered in this article. The conventional Bayesian framework as well as the Markov Chain Monte Carlo (MCMC) method to generate the Bayesian conditional probabilities of interest are discussed. Sensitivity of the prior for the model is also examined. The flood data on Fox River, Wisconsin, from 1918 to 1950, are used to illustrate all the methods of inference discussed in this article.     

Selection and Ranking Procedures for Type I Extreme Value Populations and a Related Homogeneity Test

Consider k (≥2) independent Type I extreme value populations with unknown location parameters and common known scale parameter. With samples of same size, we study procedures based on the sample means for (1) selecting the population having the largest location parameter, (2) selecting the population having the smallest location parameter, and (3) testing for equality of all the location parameters. We use Bechhofer's indifference-zone and Gupta's subset selection formulations. Tables of constants for implemention are provided based on approximation for the distribution of the standardized sample mean by a generalized Tukey's lambda distribution. Examples are provided for all procedures.     

Corrections on “Exact Bayesian Variable Sampling Plans for the Exponential Distribution Based on Type-I and Type-II Hybrid Censored Samples”

Some corrections are made for the article mentioned above. These errors occured due to the floating errors in the computation of the Bayes risk which involves terms of large magnitude and opposite sign as sample size increases, that resulted in loss of accuracy in fixed precision computational tool such as Fortran language. For accurate numerical calculation, we now use the symbolic math package, Maple, to implement the calculation which can supply numerical answers accurate to any required degree of precision. Based on the new tables, some comments made earlier in Sec. 4 have been changed suitably.     

Standard Exponential Cure Rate Model with Noninformative or Informative Uniform-Exponential Censoring

In survival data analysis it is frequent the occurrence of a significant amount of censoring to the right indicating that there may be a proportion of individuals in the study for which the event of interest will never happen. This fact is not considered by the ordinary survival theory. Consequently, the survival models with a cure fraction have been receiving a lot of attention in the recent years. In this article, we consider the standard mixture cure rate model where a fraction p ₀ of the population is of individuals cured or immune and the remaining 1 ? p ₀ are not cured. We assume an exponential distribution for the survival time and an uniform-exponential for the censoring time. In a simulation study, the impact caused by the informative uniform-exponential censoring on the coverage probabilities and lengths of asymptotic confidence intervals is analyzed by using the Fisher information and observed information matrices.     

Bias Correction in the Type I Generalized Logistic Distribution

Four strategies for bias correction of the maximum likelihood estimator of the parameters in the Type I generalized logistic distribution are studied. First, we consider an analytic bias-corrected estimator, which is obtained by deriving an analytic expression for the bias to order n ^?1; second, a method based on modifying the likelihood equations; third, we consider the jackknife bias-corrected estimator; and fourth, we consider two bootstrap bias-corrected estimators. All bias correction estimators are compared by simulation. Finally, an example with a real data set is also presented.