Computer-aided formulation and optimal control of an integrated production system for competitive products

An integrated production, inventory and advertising system has been formulated based on control engineering principles. In this system, the customer's demand is satisfied from stock, which in turn is replenished from production facilities. But sales reflect the advertising effort, present as well as past. The past effort has been considered as a delay with an assumed delay period. The problem is formulated as a state and observation model. Out of this an augmented model of state and parameters is formed. The parameters describing the model are estimated from MAP discrete filter algorithm. It is shown that sales of product 1 or product 2 at (k + l)th period is effected by sales and advertising of product 1 or product 2 at the kth period, and also by sales and advertising of product 2 or product 1 at (k-θ)th period, where 6 is the delay.     

Commuting Matrices in the Queue Length and Sojourn Time Analysis of MAP/MAP/1 Queues

Queues with Markovian arrival and service processes, i.e., MAP/MAP/1 queues, have been useful in the analysis of computer and communication systems and different representations for their stationary sojourn time and queue length distribution have been derived. More specifically, the class of MAP/MAP/1 queues lies at the intersection of the class of QBD queues and the class of semi-Markovian queues. While QBD queues have a matrix exponential representation for their queue length and sojourn time distribution of order N and N², respectively, where N is the size of the background continuous time Markov chain, the reverse is true for a semi-Markovian queue. As the class of MAP/MAP/1 queues lies at the intersection, both the queue length and sojourn time distribution of a MAP/MAP/1 queue has an order N matrix exponential representation. The aim of this article is to understand why the order N² distributions of the sojourn time of a QBD queue and the queue length of a semi-Markovian queue can be reduced to an order N distribution in the specific case of a MAP/MAP/1 queue. We show that the key observation exists in establishing the commutativity of some fundamental matrices involved in the analysis of the MAP/MAP/1 queue.     

濑尿虾真空气调包装保鲜研究

本研究用不同比例混合的O2,CO2和N2的两组混合气对濑尿虾进行真空气调包装保鲜研究,包装后的濑尿虾在保鲜期内进行感官评定,总挥发性盐基氮（TVBN）,大肠菌群、细菌总数和生化指标（K值）的检测。结果表明：在4℃左右的保存温度下,用涂布聚酯／聚乙烯（K．PET／PE）的78灿m厚的复合薄膜,用混合比例为60％C02／30％N2／10％02及混合比例为75％CO2／20％N2／5％O2的两种混合气体对濑尿虾进行真空气调保鲜包装,其保鲜期可达到12天。     

Temporary migration: a case study of Florida

Most migration statistics in the United States focus on changes in permanent residence, thereby missing temporary moves such as the daily commute to work, business trips, vacations, and seasonal migration. In this paper, we analyze temporary migration streams in Florida, focusing on moves that include an extended stay. Using several types of survey data, we examine the characteristics of non-Floridians who spend part of the year in Florida and Floridians who spend part of the year elsewhere. We develop estimates of the number, timing, and duration of temporary moves and the origins, destinations, characteristics, and motivations of temporary migrants. This study presents the most comprehensive analysis yet of temporary migration in Florida and provides a model that can be used in other places. It also points to a serious shortcoming in the US statistical system, namely, the lack of information on temporary migration streams. We believe the American Community Survey provides an opportunity to remedy this problem.     

Estimation in Semiparametric Marginal Shared Gamma Frailty Models

The semiparametric marginal shared frailty models in survival analysis have the non–parametric hazard functions multiplied by a random frailty in each cluster, and the survival times conditional on frailties are assumed to be independent. In addition, the marginal hazard functions have the same form as in the usual Cox proportional hazard models. In this paper, an approach based on maximum likelihood and expectation–maximization is applied to semiparametric marginal shared gamma frailty models, where the frailties are assumed to be gamma distributed with mean 1 and variance θ. The estimates of the fixed–effect parameters and their standard errors obtained using this approach are compared in terms of both bias and efficiency with those obtained using the extended marginal approach. Similarly, the standard errors of our frailty variance estimates are found to compare favourably with those obtained using other methods. The asymptotic distribution of the frailty variance estimates is shown to be a 50–50 mixture of a point mass at zero and a truncated normal random variable on the positive axis for θ₀ = 0. Simulations demonstrate that, for θ₀ < 0, it is approximately an x −(100 − x )%, 0 ≤ x ≤ 50, mixture between a point mass at zero and a truncated normal random variable on the positive axis for small samples and small values of θ₀; otherwise, it is approximately normal.     

Bias in Multinomial Models

This paper investigates bias in parameter estimates and residual diagnostics for parametric multinomial models by considering the effect of deleting a cell. In particular, it describes the average changes in the standardized residuals and maximum likelihood estimates resulting from conditioning on the given cells. These changes suggest how individual cell observations affect biases. Emphasis is placed on the role of individual cell observations in determining bias and on how bias affects standard diagnostic methods. Examples from genetics and log–linear models are considered. Numerical results show that conditioning on an influential cell results in substantial changes in biases.     

Tree consistency and bounds on the performance of the max-product algorithm and its generalizations

Finding the maximum a posteriori (MAP) assignment of a discrete-state distribution specified by a graphical model requires solving an integer program. The max-product algorithm, also known as the max-plus or min-sum algorithm, is an iterative method for (approximately) solving such a problem on graphs with cycles. We provide a novel perspective on the algorithm, which is based on the idea of reparameterizing the distribution in terms of so-called pseudo-max-marginals on nodes and edges of the graph. This viewpoint provides conceptual insight into the max-product algorithm in application to graphs with cycles. First, we prove the existence of max-product fixed points for positive distributions on arbitrary graphs. Next, we show that the approximate max-marginals computed by max-product are guaranteed to be consistent, in a suitable sense to be defined, over every tree of the graph. We then turn to characterizing the nature of the approximation to the MAP assignment computed by max-product. We generalize previous work by showing that for any graph, the max-product assignment satisfies a particular optimality condition with respect to any subgraph containing at most one cycle per connected component. We use this optimality condition to derive upper bounds on the difference between the log probability of the true MAP assignment, and the log probability of a max-product assignment. Finally, we consider extensions of the max-product algorithm that operate over higher-order cliques, and show how our reparameterization analysis extends in a natural manner.     

球面最小范数插值的误差估计

由球面一基本系及半内积空间构成一Hilbert函数空间,对该函数空间上的最小范数插值,给出了一致误差估计.     

Estimation of parameters of Kumaraswamy-Exponential distribution under progressive type-II censoring

In this paper, the problem of estimating unknown parameters of a two-parameter Kumaraswamy-Exponential (Kw-E) distribution is considered based on progressively type-II censored sample. The maximum likelihood (ML) estimators of the parameters are obtained. Bayes estimates are also obtained using different loss functions such as squared error, LINEX and general entropy. Lindley's approximation method is used to evaluate these Bayes estimates. Monte Carlo simulation is used for numerical comparison between various estimates developed in this paper.     

The median estimate of the autoregressive location parameter

A median-based estimate of the location (i.e. intercept) parameter in an autoregressive time series is considered. Specifically, the asymptotic joint distribution of the location estimate and a location invariant estimate of the AR parameter vector is derived. Applications of this result to rank-based estimates are briefly discussed and illustrated with a numerical example.