Bayes and Empirical Bayes Estimation of the Parameter n in a Binomial Distribution

The problem of estimating the total number of trials n in a binomial distribution is reconsidered in this article for both cases of known and unknown probability of success p from the Bayesian viewpoint. Bayes and empirical Bayes point estimates for n are proposed under the assumption of a left-truncated prior distribution for n and a beta prior distribution for p. Simulation studies are provided in this article in order to compare the proposed estimate with the most familiar n estimates.     

Confidence Intervals for Survival Probabilities: A Comparison Study

The confidence interval of the Kaplan–Meier estimate of the survival probability at a fixed time point is often constructed by the Greenwood formula. This normal approximation-based method can be looked as a Wald type confidence interval for a binomial proportion, the survival probability, using the “effective” sample size defined by Cutler and Ederer. Wald-type binomial confidence interval has been shown to perform poorly comparing to other methods. We choose three methods of binomial confidence intervals for the construction of confidence interval for survival probability: Wilson's method, Agresti–Coull's method, and higher-order asymptotic likelihood method. The methods of “effective” sample size proposed by Peto et al. and Dorey and Korn are also considered. The Greenwood formula is far from satisfactory, while confidence intervals based on the three methods of binomial proportion using Cutler and Ederer's “effective” sample size have much better performance.     

On Power Approximations and Comparison of Several Asymptotic Tests to Detect a Specified Difference between Two Proportions

A large sample test is proposed for a problem of testing for a specified difference between two binomial proportions. The test is compared to the tests by Falk and Koch (1998 Falk , R. W. , Koch , G. G. ( 1998 ). Testing a specified difference between proportions . Biometrics 54 ( 4 ): 1602 – 1614 .[Crossref] , [Google Scholar]), and Parmet and Schechtman (2007 Parmet , Y. , Schechtman , E. ( 2007 ). On a test of the difference between two binomial proportions . Communications in Statistics – Theory and Methods 36 : 887 – 895 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), and is shown to dominate in terms of the Type I error rate control. Asymptotic power is derived for each test and is shown to result in values quite proximate to the simulated power values. In addition, formulas to perform sample size estimation are provided. These methods are expected to be especially valuable in the design stage when obtaining the correct power/sample size estimation is essential.     

Distribution-Free Exceedance CUSUM Control Charts for Location

Distribution-free (nonparametric) control charts can be useful to the quality practitioner when the underlying distribution is not known. A Phase II nonparametric cumulative sum (CUSUM) chart based on the exceedance statistics, called the exceedance CUSUM chart, is proposed here for detecting a shift in the unknown location parameter of a continuous distribution. The exceedance statistics can be more efficient than rank-based methods when the underlying distribution is heavy-tailed and/or right-skewed, which may be the case in some applications, particularly with certain lifetime data. Moreover, exceedance statistics can save testing time and resources as they can be applied as soon as a certain order statistic of the reference sample is available. Guidelines and recommendations are provided for the chart's design parameters along with an illustrative example. The in- and out-of-control performances of the chart are studied through extensive simulations on the basis of the average run-length (ARL), the standard deviation of run-length (SDRL), the median run-length (MDRL), and some percentiles of run-length. Further, a comparison with a number of existing control charts, including the parametric CUSUM chart and a recent nonparametric CUSUM chart based on the Wilcoxon rank-sum statistic, called the rank-sum CUSUM chart, is made. It is seen that the exceedance CUSUM chart performs well in many cases and thus can be a useful alternative chart in practice. A summary and some concluding remarks are given.     

Bayesian adaptive bandwidth selector for multivariate discrete kernel estimator

We treat a non parametric estimator for joint probability mass function, based on multivariate discrete associated kernels which are appropriated for multivariate count data of small and moderate sample sizes. Bayesian adaptive estimation of the vector of bandwidths using the quadratic and entropy loss functions is considered. Exact formulas for the posterior distribution and the vector of bandwidths are obtained. Numerical studies indicate that the performance of our approach is better, comparing with other bandwidth selection techniques using integrated squared error as criterion. Some applications are made on real data sets.     

北京市停车换乘行为影响因素分析

基于文献综述将影响北京市私家车出行者选择停车换乘(P&R)模式的因素分为六类,通过深度访谈确定17项具体因素;通过SP调查法建立二项Logit模型筛选出对出行者选择P&R模式影响显著的因素并分析其影响机理;同时,针对与P&R设施特征相关的3项因素设计正交试验,分析出行者的敏感程度。研究结果表明:影响北京市私家车出行者选择P&R的因素有学历、职业、家庭月收入、出行距离、中心区道路拥挤水平、中心区寻找车位时间、中心区停车费、P&R车位供给以及P&R设施与公交站台之间的步行时间;出行者对P&R设施变量的敏感程度依次为P&R车位供给、P&R设施与站台间步行时间以及P&R停车费。由结论建议:北京市政府应增加P&R设施数量、合理选址、与公交紧密衔接、收费适当提高并智能化、加强宣传以及制定相关配套政策。     

Approximations to the distribution of weighted combination of independent probabilities

Two simple approximations are proposed for the distribution of the weighted combina-tion of n independent probabilities. The approximations are compared with other avail-able approximations. It is shown that one of the proposed approximations is better than the other approximations.     

On the maximum of periodic integer-valued sequences with exponential type tails via max-semistable laws

In this work we study the limiting distribution of the maximum term of periodic integer-valued sequences with marginal distribution belonging to a particular class where the tail decays exponentially. This class does not belong to the domain of attraction of any max-stable distribution. Nevertheless, we prove that the limiting distribution is max-semistable when we consider the maximum of the first k_n observations, for a suitable sequence {_kn}$\{k_n\}$ increasing to infinity. We obtain an expression for calculating the extremal index of sequences satisfying certain local conditions similar to conditions D^(m)(_un)$D^{(m)}(u_n)$, m∈N$m\in \mathbb{N}$, defined by Chernick et al. (1991). We apply the results to a class of max-autoregressive sequences and a class of moving average models. The results generalize the ones obtained for the stationary case.