A Simple Proof of the Equivalence of the Limiting Distributions of the Continuous-Time and the Embedded Process of the Queue Size in the M/G/1 Queue*

This paper presents an extremely simple proof of the known remarkable fact that for the M/G/1 queue the continuous-time process describing the number of customers in the system has the same limiting distribution as the embedded process describing the number of customers in the system just after service completion epochs.     

Regularities in the vertical arrangement of land uses in Sydney's central area

Summary

Previous studies of the vertical arrangement of land uses within the central areas of cities have been few, incomplete and employed crude methods of analysis. The present study employs 24 categories of land uses and analyses their distribution over 50 floor levels in Sydney's central district. To model the data, the gamma distribution is employed, being a flexible curve type. With only trifling exceptions, this distribution represents the data remarkably well. The two parameters of the fitted curves are interpreted as: (a) a measure of the propensity of a use to be accommodated over a wide range of floor levels, and (b) as a measure of resistance to height. The values of the parameters are used to define, using a clustering algorithm, groups of uses having members characterized by the most similar floor level arrangement. The results are of major importance for three reasons: First, the degree of regularity in the way establishments seek locations in the height dimension has not been discovered before. Second, the gamma‐distribution offers utility in modelling vertical location and should be useful in testing aspects of different town planning policies on plot ratios. Third, draconian town planning restrictions imposed on height controls may introduce locational inefficiencies hitherto unsuspected.     

Limit theorems for multivariate discrete distributions

According to the usual law of small numbers a multivariate Poisson distribution is derived by defining an appropriate model for multivariate Binomial distributions and examining their behaviour for large numbers of trials and small probabilities of marginal and simultaneous successes. The weak limit law is a generalization of Poisson's distribution to larger finite dimensions with arbitrary dependence structure. Compounding this multivariate Poisson distribution by a Gamma distribution results in a multivariate Pascal distribution which is again asymptotically multivariate Poisson. These Pascal distributions contain a class of multivariate geometric distributions. Finally the bivariate Binomial distribution is shown to be the limit law of appropriate bivariate hypergeometric distributions. Proving the limit theorems mentioned here as well as understanding the corresponding limit distributions becomes feasible by using probability generating functions.     

基于神经网络模型的智能产业板块股价探究

针对金融波动性和市场风险,基于A股市场上70余只智能板块的股票近10年的四因子数据,从神经网络模型入手实证分析,利用随机梯度算法对收盘价预测,比较预测值与实际值的模型误差及损失函数,进行因子选取、算法改进及指标择优。结果表明,神经网络模型参数在批次为2、迭代次数为4 150时,MSE(均方误差)、MAPE(平均绝对百分比误差)、MAE(平均绝对误差)分别为60.191 1、30.732 6、4.803 2,收盘价的拟合效果最佳,该参数下的神经网络模型可用于探究股票市场价格趋势,为投资者、金融机构提供一定参考依据。     

Local Powers of Optimal One‐sample and Multi‐sample Tests for the Concentration of Fisher‐von Mises‐Langevin Distributions

One‐sample and multi‐sample tests on the concentration parameter of Fisher‐von Mises‐Langevin distributions on (hyper‐)spheres have been well studied in the literature. However, only little is known about their behaviour under local alternatives, which is due to complications inherent to the curved nature of the parameter space. The aim of the present paper therefore consists in filling that gap by having recourse to the Le Cam methodology, which has recently been adapted from the linear to the spherical setup. We obtain explicit expressions of the powers for the most efficient one‐ and multi‐sample tests. As a nice by‐product, we are also able to write down the powers (against local Fisher‐von Mises‐Langevin alternatives) of the celebrated Rayleigh test of uniformity. A Monte Carlo simulation study confirms our theoretical findings and shows the empirical powers of the above‐mentioned procedures.     

GRADING JOURNALS IN ECONOMICS: THE ABCS OF THE ABDC

Many institutions and governments grade academic journals for the evaluation of research. In this paper, we implement a multi-bibliometric methodology for the evaluation of such a list of journal grades. We examine the grades assigned by the Australian Business Deans Council (ABDC) for over 750 journals in the fields of economics and statistics. Firstly, we generate up to 48 bibliometric-based grades for each journal based on the grade distribution implied by the ABDC. Secondly, we categorize the bibliometrics employing a cluster analysis of an interrater agreement statistic. Thirdly, we present a visualization of the consistency of the grading by journal. Finally, we list those journals where the majority of the matched bibliometrics indicate a higher or lower grade than their ABDC grade.     

Estimation of P[Y < X] for generalized exponential distribution

This paper deals with the estimation of P[Y < X] when X and Y are two independent generalized exponential distributions with different shape parameters but having the same scale parameters. The maximum likelihood estimator and its asymptotic distribution is obtained. The asymptotic distribution is used to construct an asymptotic confidence interval of P[Y < X]. Assuming that the common scale parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are obtained. Different confidence intervals are proposed. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of a simulated data set has also been presented for illustrative purposes.Part of the work was supported by a grant from the Natural Sciences and Engineering Research Council     

Minimax estimation under convex loss when the parameter interval is bounded

In the present paper families of truncated distributions with a Lebesgue density forx=(x ₁,...,x _n ) ε ℝ ⁿ are considered, wheref ₀:ℝ → (0, ∞) is a known continuous function andC _n (ϑ) denotes a normalization constant. The unknown truncation parameterϑ which is assumed to belong to a bounded parameter intervalΘ=[0,d] is to be estimated under a convex loss function. It is studied whether a two point prior and a corresponding Bayes estimator form a saddle point when the parameter interval is sufficiently small.     

RFID技术在汽配管理系统中的应用

针对目前汽车配件仓储销售管理中存在的问题,通过对RFID技术原理和优势进行分析,给出一种基于RFID技术的汽车配件物流管理的新模式。