Some applications of lagrangian distributions in queueing theory and epidemiology

In this note we demonstrate that the Lagrangian distributions have applications in queueing theory and theory of epidemics. The Lagrangian distribution appears as the distribution describing the number of customers served in a busy period under certain conditions. Also, the Lagrangian distribution describes the distribution of number of persons infected by a certain infectious disease.     

The effect of individual variability on the life table

A general formulation of the life table in the presence of individual jeterogeneity is presented. The possible effects of heterogeneity on the various life table functions are outlined. For the case of ordinary life tables, a method is presented for the evaluation of these effects. The proposed method id illustrated by a numerical example.     

Routing in a queueing system with two heterogeneous servers in speed and in quality of resolution

Heterogeneous servers, in manufacturing and service systems, may have different speeds and different quality levels for the provided service or good For a two-server queueing model, we formulate the job routing problem for minimizing the stationary weighted sum of the expected time spent in the system and the number of unsatisfied customers per time unit. Using a Markov decision process approach, we prove that the optimal routing policy of jobs to service is a threshold policy that depends on the queue length. When the number of waiting jobs in the queue is below a certain threshold, only one server should work and the other one remains idle. At or above this threshold, both servers should serve jobs. This is an extension of the known result where only the heterogeneity in speed is considered.     

The effect of autocorrelation on the retrospective X-chart

Quality control chart interpretation is usually based on the assumption that successive observations are independent over time. In this article we show the effect of autocorrelation on the retrospective Shewhart chart for individuals, often referred to as the X-chart, with the control limits based on moving ranges. It is shown that the presence of positive first lag autocorrelation results in an increased number of false alarms from the control chart. Negative first lag autocorrelation can result in unnecessarily wide control limits such that significant shifts in the process mean may go undetected. We use first-order autoregressive and first-order moving average models in our simulation of small samples of autocorrelated data.     

Analysis of non-repairable cold-standby systems in Bayes theory

ABSTRACT

In this paper, we seek to analyse the reliability of k-out-of-n cold-standby system with components having Weibull time-to-failure distribution in view of Bayes theory. At first, we review the existing methods exhaustively and find that all these methods have not considered Bayes theory. Then we modify the simplest method and propose new methods based on Monte Carlo simulation. Next, we combine all the information to derive the posterior distribution of Weibull parameters. A robust and universal sample-based method is proposed according to the Monte Carlo Markov Chain method to draw the sample of parameters to obtain the Bayes estimate of reliability. The drawn samples are proved to be rather satisfactory. Conducting a simulation study to compare all the methods in terms of accuracy and computational time, we have presented some useful recommendations from the simulation results. These conclusions would provide insight on the application for k-out-of-n cold-standby system.     

Generalized exchange and propensity for military service: The moderating effect of prior military exposure

The propensity for military service (PMS) of young Americans is an important issue for our Armed Forces. Since the 1990s, the PMS of young Americans has steadily declined. Overtime, a declining PMS may cause military mission degradation, lowering of military recruitment standards, base closures, and reinstatement of the unpopular military draft system. This paper investigates the moderator effect of prior military service on the Generalized Exchange-PMS relationship. Generalized exchange is when indirect benefits such as preserving freedom and the American way of life accrue to the larger society because of an individual's military service. This paper uses a structural equation modelling approach to analyse the moderating effect of prior military exposure on prospective recruits regarding their PMS. Findings indicate that the group of prospective recruits with prior military exposure had higher levels of PMS than the group without such exposure, that is, the young people with prior military exposure are more likely to enlist in the military than the young Americans with no prior military exposure.     

Bayesian prediction of waiting times in stochastic models

The authors show how saddlepoint techniques lead to highly accurate approximations for Bayesian predictive densities and cumulative distribution functions in stochastic model settings where the prior is tractable, but not necessarily the likelihood or the predictand distribution. They consider more specifically models involving predictions associated with waiting times for semi‐Markov processes whose distributions are indexed by an unknown parameter θ. Bayesian prediction for such processes when they are not stationary is also addressed and the inverse‐Gaussian based saddlepoint approximation of Wood, Booth & Butler (1993) is shown to accurately deal with the nonstationarity whereas the normal‐based Lugannani & Rice (1980) approximation cannot, Their methods are illustrated by predicting various waiting times associated with M/M/q and M/G/1 queues. They also discuss modifications to the matrix renewal theory needed for computing the moment generating functions that are used in the saddlepoint methods.     

Bayesian prediction with an asymmetric criterion in a nonparametric model of insurance risk

A median-unbiased estimator of the characteristic exponent of a symmetric stable distribution is constructed.     

The estimation uncertainty of permanent-transitory decompositions in co-integrated systems

The topic of this article is the estimation uncertainty of the Stock–Watson and Gonzalo–Granger permanent-transitory decompositions in the framework of the co-integrated vector autoregression. We suggest an approach to construct the confidence interval of the transitory component estimate in a given period (e.g., the latest observation) by conditioning on the observed data in that period. To calculate asymptotically valid confidence intervals, we use the delta method and two bootstrap variants. As an illustration, we analyze the uncertainty of (U.S.) output gap estimates in a system of output, consumption, and investment.     

层次分析法中判断矩阵的改进

通过引入计算数学迭代的思想,对层次分析法中的判断矩阵进行调整改进。使某些不能通过一致性检验的判断矩阵,重新通过检验,并用VisualBa8ic语言来实现这一过程。通过计算机的使用,使得这一方法变得方便、实用。最后,给出一简单实例来证明此方法的可行性。     

The role of the drift in I(2) systems

Summary This paper discussed the role of the drift in vector autoregressive processes allowing for integrated components up to order 2. It is shown how the drift can generate linear and quadratic deterministic trends. A two-stage statistical analysis of the system in the presence of quadratic trends is proposed. The analysis of the system allows to define a consistent sequence of tests on the numbers of common components integrated of a given order, called the integration indices of the system. The relevant asymptotic distributions are non-standard, belong to the Limiting Gaussian Functional family and are tabulated by simulation. The proposed procedure can also be consistently combined with other procedures proposed by the author for the cases of a linear trend and of no deterministic trends in the system. Invited paper at the Conference held in Bologna, Italy, 27–28 May 1993, on “Statistical Tests: Methodology and Econometric Applications”. Partial financial support is acknowledged from Italian MURST grants 40% and 60%.     

The effect of classification errors in survival data analysis

Survival data analysis aims at collecting data on durations spent in a state by a sample of units, in order to analyse the process of transition to a different state. Survival analysis applied to social and economic phenomena typically relies upon data on transitions collected, for a sample of units, in one or more follow-up surveys. We explore the effect of misclassification of the transition indicator on parameter estimates in an appropriate statistical model for the duration spent in an origin state. Some empirical investigations about the bias induced when ignoring misclassification are reported, extending the model to include the possibility that the rate of misclassification can vary across units according to the value of some covariates. Finally it is shown how a Bayesian approach can lead to parameter estimates.     

The effect of mixing-distribution misspecification in conjugate mixture models

Parametric mixture models are commonly used in the analysis of clustered data. Parametric families are specified for the conditional distribution of the response variable given a cluster-specific effect, and for the marginal distribution of the cluster-specific effects. This latter distribution is referred to as the mixing distribution. If the form of the mixing distribution is misspecified, then Bayesian and maximum-likelihood estimators of parameters associated with either distribution may be inconsistent. The magnitude of the asymptotic bias is investigated, using an approximation based on infinitesimal contamination of the mixing distribution. The approximation is useful when there is a closed-form expression for the marginal distribution of the response under the assumed mixing distribution, but not under the true mixing distribution. Typically this occurs when the assumed mixing distribution is conjugate, meaning that the conditional distribution of the cluster-specific parameter given the response variable belongs to the same parametric family as the mixing distribution.     

The limiting distribution of the least-squares estimator in nearly integrated seasonal models

We consider the least-squares estimator of the autoregressive parameter in a nearly integrated seasonal model. Building on the study by Chan (1989), who obtained the limiting distribution, we derive a closed-form expression for the appropriate limiting joint moment generating function. We use this function to tabulate percentage points of the asymptotic distribution for various seasonal periods via numerical integration. The results are extended by deriving a stochastic asymptotic expansion to order O_p(T^-l), whose percentage points are also obtained by numerically integrating the appropriate limiting joint moment generating function. The adequacy of the approximation to the finite-sample distribution is discussed.     

The role of acceptance sampling in modern quality control

Acceptance sampling procedures can be employedina program of accept ance control to achievebetterqualityat lowercost. An overview of the application of moder nacceptance samplingplans, schemes, andsys tems is described with emphas is on the iruse in facilitating process control. Sampling procedures must continually bemade to matchexist in gconditions, and to self-destruct whennolonger warranted. In this way they can be usedinane voluti on ary manne rina continuing program of acceptance control for quality improvement. Implemen- tation of process control canbefacilitated by on-going application of acceptance control to achieve the full be nefits of statistical quality control.     

Consistency of maximum likelihood estimators in a large class of deconvolution models

We consider the maximum likelihood estimator $\hat{F}_n$ of a distribution function in a class of deconvolution models where the known density of the noise variable is of bounded variation. This class of noise densities contains in particular bounded, decreasing densities. The estimator $\hat{F}_n$ is defined, characterized in terms of Fenchel optimality conditions and computed. Under appropriate conditions, various consistency results for $\hat{F}_n$ are derived, including uniform strong consistency. The Canadian Journal of Statistics 41: 98–110; 2013 © 2012 Statistical Society of Canada     

层次分析法在选择最佳零售业态的应用及其改进

在介绍层次分析法和各种零售业态特点的基础上,以天津市某个居民小区为例,说明了应用层次分析法在居民小区中选取最佳的零售业态的过程,并在此过程中,对层次分析法进行了改进。