The error in the normal approximation to the multinomial with an increasing number of classes

In an earlier paper, it was shown that under certain conditions, if the number of classes in a multinomial distribution increases as the number of trials increases, the probabilities assigned to arbitrary regions by the multinomial distribution are close to the probabilities assigned by the distribution of slightly rounded-off normal random variables. A different method of studying the approximation of the multinomial distribution by a normal distribution is to use the multivariate Berry-Esseen bound. In this paper, these two methods are compared, particularly with respect to the class of multinomial distributions for which the bounds on the error remain useful.     

The normal approximation to the multinomial with an increasing number of classes

For a fixed number of classes and the number of trials increasing, the approach of the multinomial cumulative distribution function to a normal cumulative distribution function is familiar. In this paper we allow the number of classes to increase as the number of trials increases, and show that under certain circumstances the probabilities assigned to arbitrary regions by the multinomial distribution are all close to the probabilities assigned by the distribution of “rounded off” normal random variables. As the number of trials increases, the amount rounded off approaches zero. The result can be used to study the asymptotic distribution of functions of multinomial random variables.     

Inference for the maximum cell probability under multinomial sampling

This article investigates inference for p_max, the largest cell probability in multinomial trials for the case of a small to moderate number of trials. Emphasis focuses on point and interval estimation. Both frequentist and Bayesian approaches are developed. The results of extensive simulation investigation are included as well as the analysis of a set of crime data for the city of New Orleans taken from the National Crime Survey.     

Efficient multinomial selection in simulation

Consider a simulation experiment consisting of v independent vector replications across k systems, where in any given replication one system is selected as the best performer (i.e., it wins). Each system has an unknown constant probability of winning in any replication and the numbers of wins for the individual systems follow a multinomial distribution. The classical multinomial selection procedure of Bechhofer, Elmaghraby, and Morse (Procedure BEM) prescribes a minimum number of replications, denoted as v*, so that the probability of correctly selecting the true best system (PCS) meets or exceeds a prespecified probability. Assuming that larger is better, Procedure BEM selects as best the system having the largest value of the performance measure in more replications than any other system. We use these same v* replications across k systems to form (v*)^k pseudoreplications that contain one observation from each system, and develop Procedure AVC (All Vector Comparisons) to achieve a higher PCS than with Procedure BEM. For specific small-sample cases and via a large-sample approximation we show that the PCS with Procedure AVC exceeds the PCS with Procedure BEM. We also show that with Procedure AVC we achieve a given PCS with a smaller v than the v* required with Procedure BEM. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 459–482, 1998     

A recursive algorithm for a summed multinomial density function

An algorithm for calculating the probabilities of a summed multinomial density function which is recursive with n (the number of trials) is presented. Having application in inspector error models for auditing and quality control problems with Cartesian product structures, the algorithm is discussed in the context of computing optimal economic sampling plans. Computational experience with the algorithm is presented.     

Some limiting distributions associated with sequences of multinomial trials

A series of independent trials is considered in which one of k ≥ 2 mutually exclusive and exhaustive outcomes occurs at each trial. The series terminates when m outcomes of any one type have occurred. The limiting distribution (as m → ∞) of the number of trials performed until termination is found with particular attention to the situation where a Dirichlet distribution is assigned to the k vector of probabilities for each outcome. Applications to series of races involving k runners and to spares problems in reliability modeling are discussed. The problem of selecting a stopping rule so that the probability of the series terminating on outcome i is k^?1 (i.e., a “fair” competition) is also studied. Two generalizations of the original asymptotic problem are addressed.     

基于PMC模型的神经网络

在计算机系统中有许多诊断算法,其中针对PMC模型有0-1规划的诊断算法,这个诊断算法是NP完全的,是在多项式时间内不可解的。然而利用神经网络的高度并行性这个特点,就可以在很短的时间内解出结果。主要分析了系统诊断模型PMC的症候特征,得到其充要条件,提出了新的算法,该算法具有高度的并行性,神经网络的发展为此提供了用模拟电路来实现算法的可能性,并进行了模拟验证。     

基于正交试验设计的内燃机缸套和活塞环磨合过程数学模型的建立

在对内燃机缸套和活塞环磨合过程进行试验研究的基础上,提出了基于正交试验设计的内燃机缸套-活塞环磨合过程磨损量和磨合时间的数学模型,并对试验结果进行了多元正交多项式回归分析,进而利用磨合过程的数学模型分析了各影响因素对磨合过程的影响.磨合模型的建立对确定合理的磨合时间和磨合规范,提供了理论和方法的依据.     

重离子碰撞中的量子饱和机制

分别利用胶子半经典饱和与量子饱和机制,研究了相对论重离子碰撞中净余质子产生截面的大横动量现象。通过贝塞尔函数多项式近似与辛普森求积法的结合应用,解决了对贝塞尔函数的二重高振荡积分问题。计算发现:量子饱和机制的计算结果能很好地解释布鲁克海文国家实验室的最新实验现象,从而证实了高能重离子碰撞中胶子量子饱和机制的存在。     

Explicit steady state solutions for a particular M(x)/M/1 queueing system

An explicit steady state solution is determined for the distribution of the number of customers for a queueing system in which Poisson arrivals are bulks of random size. The number of customers per bulk varies randomly between 1 and m, m arbitrary, according to a point multinomial, and customer service is exponential. Queue characteristics are given.     

一种面向涌现的比较性话题模型

提出一种CDCMLDA生成模型来实现跨文本集的话题分析,采用狄利克雷组合多项式模型(Dirichlet Compound Multinomial,DCM)对文本集中词的涌现现象进行建模,把DCM模型和LDA结合起来分析文本集之间话题的差异,采用蒙特卡罗期望最大化方法进行参数推导。在多个实际数据集中通过定性和定量的方法对模型进行评价,实验表明,模型不仅能够发现不同文本集间的异同,而且在模型困惑度指标上相对当前两种主要跨文本集的话题模型具有明显的优势。     

Information in two-stage programming under uncertainty

The random variables in two-stage programming under uncertainty are generally treated in a passive manner in that no information regarding the random variables or the process generating the random variables may be obtained. This paper develops the economics of information for the case in which the probability distributions are discrete. A multinomial process is assumed to generate the random variables, and the parameter vector of that process is assumed to be unknown. A Dirichlet prior distribution on the parameter vector is used, and the computation of the value of information thus involves a Dirichlet-multinomial distribution on the random variables. An example involving producing to meet uncertain demands is presented.     

Power series expansions for the distribution and mean value function of a geometric process with Weibull interarrival times

The geometric process is considered when the distribution of the first interarrival time is assumed to be Weibull. Its one‐dimensional probability distribution is derived as a power series expansion of the convolution of the Weibull distributions. Further, the mean value function is expanded into a power series using an integral equation. © 2014 Wiley Periodicals, Inc. Naval Research Logistics, 61: 599–603, 2014     

The multivariate Polya distribution in combat modeling

This paper investigates the multivariate Polya distribution (MPD) for application in combat models for which enemy targets must be randomly assigned to fighting units. Six sets of actual combat data motivate the allocation model. Scenarios include air‐to‐air combat, tank, and submarine warfare. Goodness of fit tests are derived which verify the validity of the MPD, and reinforce the notion that multinomial allocation is too simplistic for such combat models. Simulations to determine optimal allocations for minimal combat cost are applied in order to illustrate the role of the MPD in combat modeling. © 2001 John Wiley & Sons,Inc. Naval Research Logistics 48: 1–17, 2001     

Supply licensing when the manufacturer strategically commits to invest in R&D

This article proposes a strategic reason for a proprietary component supplier to license her technology to a competitor or a manufacturer: her anticipation of the manufacturer's strategic commitment to invest in research and development (R&D). We address this phenomenon with a game theoretic model. Our results show that the manufacturer's full commitment to invest in R&D enables the supplier to license, sell a larger quantity through the supply chain, and charge lower prices. These results are robust to the type of demand uncertainty faced by the manufacturer within the class of increasing generalized failure rate distributions. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 341–350, 2014     

Directional change‐point detection for process control with multivariate categorical data

Most modern processes involve multiple quality characteristics that are all measured on attribute levels, and their overall quality is determined by these characteristics simultaneously. The characteristic factors usually correlate with each other, making multivariate categorical control techniques a must. We study Phase I analysis of multivariate categorical processes (MCPs) to identify the presence of change‐points in the reference dataset. A directional change‐point detection method based on log‐linear models is proposed. The method exploits directional shift information and integrates MCPs into the unified framework of multivariate binomial and multivariate multinomial distributions. A diagnostic scheme for identifying the change‐point location and the shift direction is also suggested. Numerical simulations are conducted to demonstrate the detection effectiveness and the diagnostic accuracy.© 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

A note on the forecast performance of temporal aggregation

Earlier research on the effects of nonoverlapping temporal aggregation on demand forecasting showed the benefits associated with such an approach under a stationary AR(1) or MA(1) processes for decision making conducted at the disaggregate level. The first objective of this note is to extend those important results by considering a more general underlying demand process. The second objective is to assess the conditions under which aggregation may be a preferable approach for improving decision making at the aggregate level as well. We confirm the validity of previous results under more general conditions, and we show the increased benefit resulting from forecasting by temporal aggregation at lower frequency time units. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 489–500, 2014     

A note on signature‐based expressions for the entropy of mixed r‐out‐of‐ n systems

We provide an expression for the Shannon entropy of mixed r‐out‐of‐ n systems when the lifetimes of the components are independent and identically distributed. The expression gives the system's entropy in terms of the system signature, the distribution and density functions of the lifetime model, and the information measures of the beta distribution. Bounds for the system's entropy are obtained by direct applications of the concavity of the entropy and the information inequality.Copyright © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 202–206, 2014     

Joint pricing,assortment, and inventory decisions for a retailer's product line

Consider a set of product variants that are differentiated by some secondary attributes such as flavor, color, or size. The retailer's problem is to jointly determine the set of variants to include in her product line (“assortment”), together with their prices and inventory levels, so as to maximize her expected profit. We model the consumer choice process using a multinomial logit choice model and consider a newsvendor type inventory setting. We derive the structure of the optimal assortment for some important special cases, including the case of horizontally differentiated items, and propose a dominance relationship for the general case that simplifies the search for an optimal assortment. We also discuss structural properties of the optimal prices. Finally, motivated by our analytical results, we propose a heuristic solution procedure, which is shown to be quite effective through a numerical study. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Power-sharing,commitment problems,and armed conflict in Ukraine

Why did the Ukraine’s 2004 Orange Revolution initiate a peaceful democratic transition, while the 2014 protests were followed by violent conflict? This article complements previous studies on Russia’s role in Ukraine by focusing on domestic explanations of the recent violence. It shows that structural factors were already conducive to violence in 2004, making it fruitful to analyse the role of agency to explain the 2014 conflict. It demonstrates that while the 2004 transition introduced power-sharing guarantees that mitigated commitment problems for the relevant parties, the 2014 transition saw no such guarantees, making violence a rational strategy for the pro-Russian separatists.