Statistical analysis of queueing systems

This paper provides an overview of the literature on statistical analysis of queueing systems. Topics discussed include: model identification, estimation, hypothesis testing and other related aspects. Not all of these statistical problems are covered in books on queueing theory or stochastic processes. The bibliography is not exhaustive, but comprehensive enough to provide sources from the literature.     

Statistical analysis of first-order MARMA processes

In this paper, we consider processes of the MARMA type that can be derived from the classical ARMA processes by replacing summation by the maximum operation. It is assumed that the innovations and the values of the process have the standard Fréchet distribution. For simple MARMA processes of first order, certain numerical characteristics are calculated. Sign tests and rank statistical methods for parameter estimation are developed. The characterization relations that can be used for the identification of models are justified.     

Statistical analysis of dyadic stationary processes

In this paper we consider a multiple dyadic stationary process with the Walsh spectral density matrix f(), where is an unknown parameter vector. We define a quasi-maximum likelihood estimator % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGabeiUdyaaja% aaaa!377D!\[{\rm{\hat \theta }}\] of , and give the asymptotic distribution of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGabeiUdyaaja% aaaa!377D!\[{\rm{\hat \theta }}\] under appropriate conditions. Then we propose an information criterion which determines the order of the model, and show that this criterion gives a consistent order estimate. As for a finite order dyadic autoregressive model, we propose a simpler order determination criterion, and discuss its asymptotic properties in detail. This criterion gives a strong consistent order estimate. In Section 5 we discuss testing whether an unknown parameter satisfies a linear restriction. Then we give the asymptotic distribution of the likelihood ratio criterion under the null hypothesis.This work is supported by Contract N00014-85-K-0292 of the Office of Naval Research and Contract F49620-85-C-0008 of the Air Force Office of Scientific Research. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notations hereon.The work of this author was done at the Center for Multivariate Analysis. His permanent address is Department of Mathematics, Hiroshima University, Hiroshima 730, Japan.     

Statistical analysis of local search landscapes

This paper discusses the application of some statistical estimation tools in trying to understand the nature of the combinatorial landscapes induced by local search methods. One interesting property of a landscape is the number of optima that are present. In this paper we show that it is possible to compute a confidence interval on the number of independent local searches needed to find all optima. By extension, this also expresses the confidence that the global optimum has been found. In many cases, this confidence may be too low to be acceptable, but it is also possible to estimate the number of optima that exist. Theoretical analysis and empirical studies are discussed, which show that it may be possible to obtain a fairly accurate picture of this property of a combinatorial landscape. The approach is illustrated by analysis of an instance of the flowshop scheduling problem.     

Statistical analysis of the generalized linear proportional hazards model

We analyze finite sample properties of modified partial likelihood estimators of parameters for the generalized proportional hazards model by simulation. A goodness-of-fit test for the proportional hazards model against the GPH model is proposed. Lung cancer data are analyzed. Bibliography: 7 titles.Published in Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 5–18     

Statistical and structural analysis of the appearance of prime numbers

We examine the distribution of the ratio of addition to multiplication over standard atomic sets of integers. By analyzing the array of conversion ratios and selected sub-arrays, we prove that the reciprocal of the mean of the conversion ratio distribution converges to the prime-counting function π(n). We also show that the modified mean of the sub-array C ⁵, which is obtained from the array of conversion ratios by scaling and translation, converges to π(n) with an accuracy comparable to the Li-function. We go on to numerically show that the relative behaviors of L(n), $1/H_{n}^{5}$ and Li(n) with respect to π(n) are similar, and that π(n)/L(n), $\pi(n)/(1/H_{n}^{5})$ and π(n)/Li(n) provide approximations of competitive accuracy at the center of the distribution.     

Statistical analysis of grouped and censored observations

The asymptotic normality and asymptotic effectiveness of generalized Bayesian estimates are proved under less restrictive hypotheses.Translated from Staticheskie Metody, pp. 122–137, 1978.     

Gamma分布环境因子的统计分析

证明了Gamma分布环境因子的最大似然估计是有偏估计,且其偏差为正,进而导出了Gamma分布环境因子的近似无偏估计.利用Cornish-Fisher展开导出了Gamma分布环境因子的广义置信区间,另外也给了Gamma分布环境因子的Bootstrap-t置信区间.利用模拟方法研究了所给近似无偏估计和区间估计的精度,模拟结果显示所给近似无偏估计和区间估计的精度是相当好的.     

Learning the coordinate gradients

In this paper we study the problem of learning the gradient function with application to variable selection and determining variable covariation. Firstly, we propose a novel unifying framework for coordinate gradient learning from the perspective of multi-task learning. Various variable selection methods can be regarded as special instances of this framework. Secondly, we formulate the dual problems of gradient learning with general loss functions. This enables the direct application of standard optimization toolboxes to the case of gradient learning. For instance, gradient learning with SVM loss can be solved by quadratic programming (QP) routines. Thirdly, we propose a novel gradient learning formulation which can be cast as a learning the kernel matrix problem. Its relation with sparse regularization is highlighted. A semi-infinite linear programming (SILP) approach and an iterative optimization approach are proposed to efficiently solve this problem. Finally, we validate our proposed approaches on both synthetic and real datasets.     

模拟随机数统计性质比较

本文总结了几种历史上有影响的模拟随机数发生方法 ,并对线性同余法和取小数法进行了统计比较 ,从而肯定了取小数法的优良性能     

Statistical analysis of two-parameter generalized Birnbaum-Saunders Cauchy distribution

The image features of density function and failure rate function are studied in detail for two-parameter generalized Birnbaum-Saunders Cauchy fatigue life distribution. The logarithmic moment estimation and other two point estimations of parameters are proposed under full sample, and the precisions of point estimations are investigated by Monte-Carlo simulations. The approximate interval estimations of parameters are given by using Taylor expansion, and the precisions of approximate interval estimations are investigated by Monte-Carlo simulations. Finally, several examples show the feasibility of the methods.     

Statistical analysis of autoregressive fractionally integrated moving average models in R

The autoregressive fractionally integrated moving average (ARFIMA) processes are one of the best-known classes of long-memory models. In the package afmtools for R, we have implemented a number of statistical tools for analyzing ARFIMA models. In particular, this package contains functions for parameter estimation, exact autocovariance calculation, predictive ability testing and impulse response function computation, among others. Furthermore, the implemented methods are illustrated with applications to real-life time series.     

A new study on the thick disk population component of the Galaxy

The newly-raised problem as to whether our Galaxy may contain a thick disk population component has aroused great interest. But up until now no conclusion has been reached unanimously for lack of observed data. Here this problem is discussed based on seven Basel field data calibrated recently and strong evidence is provided. New results on the values of structural parameters, luminosity functions and metal structure of the thick disk are also presented.     

Statistical convergence, selection principles and asymptotic analysis

We consider the set of sequences of positive real numbers in the context of statistical convergence/divergence and show that some subclasses of have certain nice selection and game-theoretic properties.     

Statistical analysis of stochastic resonance with ergodic diffusion noise

A subthreshold signal is transmitted through a channel and may be detected when some noise--with known structure and proportional to some level--is added to the data. There is an optimal noise level, called stochastic resonance that corresponds to the highest Fisher information in the problem of estimation of the signal. As noise we consider an ergodic diffusion process and the asymptotic is considered as time goes to infinity. We propose consistent estimators of the subthreshold signal and we solve further a problem of hypotheses testing. We also discuss evidence of stochastic resonance for both estimation and hypotheses testing problems via examples.     

Statistical analysis of the bearing capacity of rim-spoke flywheels made of reinforced plastics

Conclusion The suggested numerical method makes it possible to plot the distribution functions of the bearing capacity of RSF at the structural level of their design elements (rim, spokes) with a view to the scatter of the strength and strain properties of the used materials and the geometry of arrangement of the structure. This involves taking into account the random nature of the radial distribution in the rim material of both strain and strength properties, which makes it possible to investigate more fully the processes of failure really occurring in RSF. The suggested method is the basis for stipulating a scientifically substantiated safety factor (the theoretical bearing capacity) in dependence on the required reliability; this makes it possible to use a differentiated approach to problems of devising RSF for actual purposes. Our investigations may serve as the basis for solving problems of optimal planning of RSF according to the conditions of the required reliability.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1041–1047, November–December, 1987.     

我国普通高等教育人力资源发展水平的统计分析

本文综合运用主成分分析和因子分析两种综合评价方法 ,对我国各地区高等教育人力资源的发展水平进行排序和分类 ,为规划和发展各地区的高等教育事业提供了一定的科学依据。两种综合评价方法的综合运用克服了单一评价方法的片面性 ,评价结果较为全面、客观