带工期指派的产品服务系统订单随机调度问题研究

针对由一个制造工厂和多个区域服务中心组成的服务型制造企业，研究了考虑生产时间和服务时间均具有随机性且工期可指派的产品服务系统（PSS）订单调度问题。首先以最小化订单提前、误工和工期指派费用的期望总额为目标构建问题的优化模型，然后分析目标函数近似值的最优性条件，据此提出加权最短平均生产时间排序规则，并结合该规则与插入邻域局部搜索设计了启发式算法对问题进行求解，最后通过数值仿真验证算法的可行性和有效性。研究表明，提前费用偏差对PSS订单调度与工期指派决策的影响很小，因此企业管理者无需准确估计库存费用也能制定出比较有效的PSS订单调度策略；而工期指派费用偏差对决策结果的影响非常大，因此企业管理者在决策时必须谨慎估计该项费用。     

Asymptotic behaviour of binned kernel density estimators for locally non-stationary random fields

We investigate the asymptotic behaviour of binned kernel density estimators for dependent and locally non-stationary random fields converging to stationary random fields. We focus on the study of the bias and the asymptotic normality of the estimators. A simulation experiment conducted shows that both the kernel density estimator and the binned kernel density estimator have the same behavior and both estimate accurately the true density when the number of fields increases. We apply our results to the 2002 incidence rates of tuberculosis in the departments of France.     

Precise large deviations for the difference of two sums of END random variables with heavy tails

Assume that there are two types of insurance contracts in an insurance company, and the ith related claims are denoted by {X_ij, j ? 1}, i = 1, 2. In this article, the asymptotic behaviors of precise large deviations for non random difference ∑^n₁(t)_{j = 1}X_1j ? ∑^n₂(t)_{j = 1}X_2j and random difference ∑^N₁(t)_{j = 1}X_1j ? ∑^N₂(t)_{j = 1}X_2j are investigated, and under several assumptions, some corresponding asymptotic formulas are obtained.     

On the enumeration of rectangular (0, 1)-matrices

The construction and enumeration of (0, 1)-matrices with given line-sums is described for the rectangular cases often encountered in applications. Improved approximations are provided for the number of such matrices. Some new enumeration results for semi-regular bipartite graphs are included, and the related category of the quasi-semiregular bipartite graphs is recognized. The range of certain elements of products of a (0, I)-matrix is considered as a function of the line-sums. This, in turn, is related to the range in the numbers of interchanges available. Improvements in statistical practice that come from these constructions and enumerations are described.     

Complete convergence and the strong laws of large numbers for pairwise NQD random variables

The authors study the strong convergence for sequences of pairwise negatively quadrant dependent (NQD) random variables under some wide conditions, and present some new theorems on the complete convergence and the strong laws of large numbers. The obtained results extend and improve some theorems in existing literature.     

A robust automatic clustering algorithm for probability density functions with application to categorizing color images

This study develops a robust automatic algorithm for clustering probability density functions based on the previous research. Unlike other existing methods that often pre-determine the number of clusters, this method can self-organize data groups based on the original data structure. The proposed clustering method is also robust in regards to noise. Three examples of synthetic data and a real-world COREL dataset are utilized to illustrate the accurateness and effectiveness of the proposed approach.     

Estimation and simulation of conditional hazard function in the quasi-associated framework when the observations are linked via a functional single-index structure

We consider the estimation of the conditional hazard function of a scalar response variable Y given a Hilbertian random variable X when the observations are linked via a single-index structure in the quasi-associated framework. We establish the pointwise almost complete convergence and the uniform almost complete convergence (with the rate) of the estimate of this model. A simulation is given to illustrate the good behavior in the practice of our methodology.     

Conditional Akaike Information Criteria for a Class of Poisson Mixture Models with Random Effects

Focusing on the model selection problems in the family of Poisson mixture models (including the Poisson mixture regression model with random effects and zero‐inflated Poisson regression model with random effects), the current paper derives two conditional Akaike information criteria. The criteria are the unbiased estimators of the conditional Akaike information based on the conditional log‐likelihood and the conditional Akaike information based on the joint log‐likelihood, respectively. The derivation is free from the specific parametric assumptions about the conditional mean of the true data‐generating model and applies to different types of estimation methods. Additionally, the derivation is not based on the asymptotic argument. Simulations show that the proposed criteria have promising estimation accuracy. In addition, it is found that the criterion based on the conditional log‐likelihood demonstrates good model selection performance under different scenarios. Two sets of real data are used to illustrate the proposed method.     

Sum,product and ratio of Pareto and gamma variables

The exact distributions of X+Y, X Y and X/(X+Y) are studied when X and Y are independent Pareto and gamma random variables. Applications are discussed, to real problems in clinical trials, computer networks and economics.