A note on LeCam’s bound for the distance between the Poisson binomial and the Poisson distribution

n possibly different success probabilities p ₁, p ₂, ..., p _n is frequently approximated by a Poisson distribution with parameter λ = p ₁ + p ₂ + ... + p _n . LeCam's bound p ² ₁ + p ² ₂ + ... + p _n ² for the total variation distance between both distributions is particularly useful provided the success probabilities are small. The paper presents an improved version of LeCam's bound if a generalized d-dimensional Poisson binomial distribution is to be approximated by a compound Poisson distribution. Received: May 10, 2000; revised version: January 15, 2001     

二项式函数在组合恒等式证明中的应用

一些恒等式在函数论、组合数学、解析数论等学科的研究领域中极为重要。以二项式作为生成函数,给出了几个组合恒等式证明。     

Estimation from Zero-Failure Data

When performing quantitative (or probabilistic) risk assessments, it is often the case that data for many of the potential events in question are sparse or nonexistent. Some of these events may be well-represented by the binomial probability distribution. In this paper, a model for predicting the binomial failure probability, P , from data that include no failures is examined. A review of the literature indicates that the use of this model is currently limited to risk analysis of energetic initiation in the explosives testing field. The basis for the model is discussed, and the behavior of the model relative to other models developed for the same purpose is investigated. It is found that the qualitative behavior of the model is very similar to that of the other models, and for larger values of n (the number of trials), the predicted P values varied by a factor of about eight among the five models examined. Analysis revealed that the estimator is nearly identical to the median of a Bayesian posterior distribution, derived using a uniform prior. An explanation of the application of the estimator in explosives testing is provided, and comments are offered regarding the use of the estimator versus other possible techniques.     

带有快速反应策略供应链系统的补偿策略研究

过长的订购提前期往往使得零售商订货决策感到困难. 快速反应策略能使零售商在获 得更多更准确的市场需求信息后,调整订购量而提高收益. 但是快速反应策略并不一定使供应 商的利润也提高. 有文章指出只有低的服务水平才能使两者利润同时提高,因而这种方法在工 业应用中是不一定可行的. 补偿策略是一种广泛应用的方法,能够提高产品的客户服务水平, 因而研究了补偿策略在快速反应供应链系统中的作用. 在某些条件下,在快速反应供应链系统 中,补偿策略能使零售商与供应商一方的收益不变或者提高,另一方的收益有所提高,即Pare2 to 提高. 还研究了引进补偿策略后,供应链系统的最优解及期望卖出量、期望缺货量和期望残 余量的变化情况.     

Three‐Stage Decision‐Making Model under Restricted Conditions for Emergency Response to Ships Not under Control

A ship that is not under control (NUC) is a typical incident that poses serious problems when in confined waters close to shore. The emergency response to NUC ships is to select the best risk control options, which is a challenge in restricted conditions (e.g., time limitation, resource constraint, and information asymmetry), particularly in inland waterway transportation. To enable a quick and effective response, this article develops a three‐stage decision‐making framework for NUC ship handling. The core of this method is (1) to propose feasible options for each involved entity (e.g., maritime safety administration, NUC ship, and ships passing by) under resource constraint in the first stage, (2) to select the most feasible options by comparing the similarity of the new case and existing cases in the second stage, and (3) to make decisions considering the cooperation between the involved organizations by using a developed Bayesian network in the third stage. Consequently, this work provides a useful tool to achieve well‐organized management of NUC ships.     

Assessment of modeling longitudinal binary data based on graphical methods

Longitudinal categorical data are commonly applied in a variety of fields and are frequently analyzed by generalized estimating equation (GEE) method. Prior to making further inference based on the GEE model, the assessment of model fit is crucial. Graphical techniques have long been in widespread use for assessing the model adequacy. We develop alternative graphical approaches utilizing plots of marginal model-checking condition and local mean deviance to assess the GEE model with logit link for longitudinal binary responses. The applications of the proposed procedures are illustrated through two longitudinal binary datasets.     

利用伪随机信号系统辨识钻柱系统

用白噪声信号作为输入信号对钻柱系统脉冲响应进行辨识。研究了伪随机信号的特征及伪随机信号产生的方法,得出了用伪随机信号代替白噪声信号辨识钻柱系统脉冲响应的结论。结合输入信号和输出信号,利用钻柱系统的脉冲响应,讨论了钻柱的临界转速、钻柱共振、钻柱与井壁之间的相互作用、所钻地层岩性等钻井工程问题。     

Dose‐Response Models Incorporating Aerosol Size Dependency for Francisella tularensis

The effect of bioaerosol size was incorporated into predictive dose‐response models for the effects of inhaled aerosols of Francisella tularensis (the causative agent of tularemia) on rhesus monkeys and guinea pigs with bioaerosol diameters ranging between 1.0 and 24 μm. Aerosol‐size‐dependent models were formulated as modification of the exponential and β‐Poisson dose‐response models and model parameters were estimated using maximum likelihood methods and multiple data sets of quantal dose‐response data for which aerosol sizes of inhaled doses were known. Analysis of F. tularensis dose‐response data was best fit by an exponential dose‐response model with a power function including the particle diameter size substituting for the rate parameter k scaling the applied dose. There were differences in the pathogen's aerosol‐size‐dependence equation and models that better represent the observed dose‐response results than the estimate derived from applying the model developed by the International Commission on Radiological Protection (ICRP, 1994) that relies on differential regional lung deposition for human particle exposure.     

Treatment Choice With Trial Data: Statistical Decision Theory Should Supplant Hypothesis Testing

Abstract

A central objective of empirical research on treatment response is to inform treatment choice. Unfortunately, researchers commonly use concepts of statistical inference whose foundations are distant from the problem of treatment choice. It has been particularly common to use hypothesis tests to compare treatments. Wald’s development of statistical decision theory provides a coherent frequentist framework for use of sample data on treatment response to make treatment decisions. A body of recent research applies statistical decision theory to characterize uniformly satisfactory treatment choices, in the sense of maximum loss relative to optimal decisions (also known as maximum regret). This article describes the basic ideas and findings, which provide an appealing practical alternative to use of hypothesis tests. For simplicity, the article focuses on medical treatment with evidence from classical randomized clinical trials. The ideas apply generally, encompassing use of observational data and treatment choice in nonmedical contexts.     

Bittersweet and Paradoxical

The American Red Cross is the most active nonprofit organization involved in disaster planning and response in the United States. The organization deployed nearly 50,000 volunteers to provide essential support to victims of some 125,000 domestic disasters, including home fires, hurricanes, wildfires, and floods, in a recent two‐year period. This study asks how American Red Cross disaster response volunteer experiences function to cultivate satisfaction and, at the other end of the spectrum, the kind of dissatisfaction that leads people to quit; it pays particular attention to ways in which volunteer management shapes dissatisfaction and fatigue because of implications for volunteer retention. Paradoxically, the Red Cross facilitates the highly satisfying act of helping victims, but volunteers feel dissatisfied when management practices get in the way of helping. The study suggests voluntary organizations that rely on skilled, long‐term volunteers to deliver services should evaluate and strengthen their communication strategies, recognition practices, and support systems for volunteers in distress.