CUSUM Control Charts for Multivariate Poisson Distribution

A cumulative sum control chart for multivariate Poisson distribution (MP-CUSUM) is proposed. The MP-CUSUM chart is constructed based on log-likelihood ratios with in-control parameters, Θ₀, and shifts to be detected quickly, Θ₁. The average run length (ARL) values are obtained using a Markov Chain-based method. Numerical experiments show that the MP-CUSUM chart is effective in detecting parameter shifts in terms of ARL. The MP-CUSUM chart with smaller Θ₁ is more sensitive than that with greater Θ₁ to smaller shifts, but more insensitive to greater shifts. A comparison shows that the proposed MP-CUSUM chart outperforms an existing MP chart.     

A new prototype system for optimized job shop scheduling

Optimal scheduling of shopfloor activities in an environment of discrete part manufacturing is discussed. The scheduling problem is a well known NP complete one. The main part, the sequencing problem, has been tackled using two techniques: virtual resources identification and taboo search heuristics. The first approach allowed the authors to reduce the complexity of the sequencing from a job shop to a general flow shop problem. On the other hand, the search for an optimal solution, with respect to a fixed strategy, has been achieved via the taboo search. A synthesis of the results of a large number of tests is presented as well as the results of an application to a real case. The latter is shown in comparison with the output of the system being presently used in the examined factory.     

Recent and classical goodness-of-fit tests for the Poisson distribution

We give a critical synopsis of classical and recent tests for Poissonity, our emphasis being on procedures which are consistent against general alternatives. Two classes of weighted Cramér–von Mises type test statistics, based on the empirical probability generating function process, are studied in more detail. Both of them generalize already known test statistics by introducing a weighting parameter, thus providing more flexibility with regard to power against specific alternatives. In both cases, we prove convergence in distribution of the statistics under the null hypothesis in the setting of a triangular array of rowwise independent and identically distributed random variables as well as consistency of the corresponding test against general alternatives. Therefore, a sound theoretical basis is provided for the parametric bootstrap procedure, which is applied to obtain critical values in a large-scale simulation study. Each of the tests considered in this study, when implemented via the parametric bootstrap method, maintains a nominal level of significance very closely, even for small sample sizes. The procedures are applied to four well-known data sets.     

Subjective Distributions

A decision maker has to choose one of several random variables whose distributions are not known. As a Bayesian, she behaves as if she knew the distributions. In this paper we suggest an axiomatic derivation of these (subjective) distributions, which is more economical than the derivations by de Finetti or Savage. Whereas the latter derive the whole joint distribution of all the available random variables, our approach derives only the marginal distributions. Correspondingly, the preference questionnaire needed in our case is less smaller.     

Perfect simulation for correlated Poisson random variables conditioned to be positive

In this paper we present a perfect simulation method for obtaining perfect samples from collections of correlated Poisson random variables conditioned to be positive. We show how to use this method to produce a perfect sample from a Boolean model conditioned to cover a set of points: in W.S. Kendall and E. Thönnes (Pattern Recognition 32(9): 1569–1586, 1999), this special case was treated in a more complicated way. The method is applied to several simple examples where exact calculations can be made, so as to check correctness of the program using ²-tests, and some small-scale experiments are carried out to explore the behaviour of the conditioned Boolean model.     

Confidence curves and improved exact confidence intervals for discrete distributions

The author describes a method for improving standard “exact” confidence intervals in discrete distributions with respect to size while retaining correct level. The binomial, negative binomial, hypergeometric, and Poisson distributions are considered explicitly. Contrary to other existing methods, the author's solution possesses a natural nesting condition: if α < α', the 1 ‐ α' confidence interval is included in the 1 ‐ α interval. Nonparametric confidence intervals for a quantile are also considered.     

A formulation of the concept of probability based on the use of experimental devices

This paper sets out to identify the abilities that a person needs to be able to successfully use an experimental device, such as a probability wheel or balls in an urn, for the elicitation of subjective probabilities. It is assumed that the successful use of the device requires that the person elicits unique probability values that obey the standard probability laws. This leads to a definition of probability based on the idea of the similarity between the likeliness of events and this concept is naturally extended to the idea that probabilities have strengths, which relates to information about the likeliness of an event that lies beyond a simple probability value. The latter notion is applied to the problem of explaining the Ellsberg paradox. To avoid the definition of probability being circular, probabilities are defined such that they depend on the choice of a reference set of events R which, in simple cases, corresponds to the raw outcomes produced by using an experimental device. However, it is shown that even when the events in R are considered as having an “equal chance” of occurring, the values and/or strengths of probabilities can still be affected by the choice of the set R.     

Extension of the Application of Conway‐Maxwell‐Poisson Models: Analyzing Traffic Crash Data Exhibiting Underdispersion

The objective of this article is to evaluate the performance of the COM‐Poisson GLM for analyzing crash data exhibiting underdispersion (when conditional on the mean). The COM‐Poisson distribution, originally developed in 1962, has recently been reintroduced by statisticians for analyzing count data subjected to either over‐ or underdispersion. Over the last year, the COM‐Poisson GLM has been evaluated in the context of crash data analysis and it has been shown that the model performs as well as the Poisson‐gamma model for crash data exhibiting overdispersion. To accomplish the objective of this study, several COM‐Poisson models were estimated using crash data collected at 162 railway‐highway crossings in South Korea between 1998 and 2002. This data set has been shown to exhibit underdispersion when models linking crash data to various explanatory variables are estimated. The modeling results were compared to those produced from the Poisson and gamma probability models documented in a previous published study. The results of this research show that the COM‐Poisson GLM can handle crash data when the modeling output shows signs of underdispersion. Finally, they also show that the model proposed in this study provides better statistical performance than the gamma probability and the traditional Poisson models, at least for this data set.     

英语情态动词的时态表征

针对英语情态动词有无时态形式,这一语言学界存在着较大争议的问题,从形式表征和语义表征方面入手,借助语言学历时及共时的观点,提出并论证了情态动词在形与意都具有时态的特征.     

Anderson's classification statistic based on a post-stratified training sample

The performance of Anderson's classification statistic based on a post-stratified random sample is examined. It is assumed that the training sample is a random sample from a stratified population consisting of two strata with unknown stratum weights. The sample is first segregated into the two strata by post-stratification. The unknown parameters for each of the two populations are then estimated and used in the construction of the plug-in discriminant. Under this procedure, it is shown that additional estimation of the stratum weight will not seriously affect the performance of Anderson's classification statistic. Furthermore, our discriminant enjoys a much higher efficiency than the procedure based on an unclassified sample from a mixture of normals investigated by Ganesalingam and McLachlan (1978).