Download or read book The Continuous Time Bayes Sequential Procedure for Estimating the Arrival Rate of a Poisson Process and Large Sample Properties written by C. P. Shapiro and published by . This book was released on 1977 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let X(t), t> or = 0, be a homogeneous Poisson process with arrival rate Theta. Sequential estimation procedures (sigma, Theta bar sub sigma) are considered with loss due to estimation of L(Theta, Theta bar) = 1/Theta (Theta-Theta bar)squared, and sampling costs involving both time and arrival costs. In this context the Bayes', sequential procedure is obtained in a simple computable form. The large sample properties of the procedure are then studied when Theta is fixed but unknown, and the Bayes' stopping rule tau is shown to be asymptotically equivalent to the best fixed sample size procedure when Theta is known. Asymptotic normality of the Bayes' sequential estimator Theta bar sub tau of Theta is also shown. (Author).
Download or read book Large Sample Properties of the Bayes Sequential Procedure for Estimating the Arrival Rate of a Poisson Process with Invariant Loss written by C. P. Shapiro and published by . This book was released on 1977 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let W sub n, n=0,1, ..., be the time until the nth arrival of a Poisson process with rate Theta. Using invariant loss L(Theta, Theta bar) =1/theta (Theta-Theta bar) squared and sampling costs involving cost per arrival and cost per unit time, the Bayes' sequential procedure (N*, Theta bar sub N*) is derived. The large sample properties of the procedure are then studied in the classical framework, and N*, the stopping time, is shown to be asymptotically equivalent to n*, the best fixed sample size procedure when Theta is known. Asymptotically normality of the sequential estimator Theta bar sub N* is also shown. (Author).
Download or read book Bayes Sequential Estimation Procedures for Life Testing Problems written by Evan Eva Chen and published by . This book was released on 1979 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book MRC Technical Summary Report written by United States. Army. Mathematics Research Center and published by . This book was released on 1984 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Publications of the Mathematics Research Center July 1 1975 Thru December 31 1985 written by University of Wisconsin--Madison. Mathematics Research Center and published by . This book was released on 1985 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynkin s Identity Applied to Bayes Sequential Estimation of a Poisson Process written by C. P. Shapiro and published by . This book was released on 1977 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conditional on the value of theta, theta> 0, let X(t), t> 0, be a homogeneous Poisson process. Sequential estimation procedures of the form (sigma, theta-bar(sigma)) are considered. To measure loss due to estimation, a family of functions, indexed by p, is used: L(theta, theta-bar) = theta to the -pth power (theta-theta-bar) squared, and the cost of sampling involves cost per arrival and cost per unit time. The notion of monotone case for total cost functions a continuous time process is defined in terms of the characteristic operator of the process at the total cost function. The Bayes' sequential procedure is then derived for those cost functions in the monotone case using extensions of Dynkin's identity for the characteristic operator. The properties of these procedures are studied as sampling costs tend to 0, and the procedures are then modified and compared with procedures which are optimal among all stopping rules terminating at arrivals. (Author).
Download or read book Statistical Theory and Method Abstracts written by and published by . This book was released on 1979 with total page 1268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Announcements Index written by and published by . This book was released on 1977-10-28 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Comparison of Sampling Plans for Bayesian Estimation of a Poisson Process Rate written by Robert L. Wardrop and published by . This book was released on 1979 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayes estimation of the arrival rate of a Poisson process is studied in this paper. For any loss function in the family L sub p, a simple sequential procedure Tau sub p is introduced which, based on the criterion of minimizing expected cost (estimation error plus sampling cost), is either optimal or asymptotically optimal. The procedure Tau sub p is compared to Type 1 and 2 censoring - the comparison should be useful to experimenters choosing between the three sampling plans.
Download or read book Government Reports Annual Index written by and published by . This book was released on 1977 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 1981 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1969 with total page 1508 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NBS Special Publication written by and published by . This book was released on 1970 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to the Statistics of Poisson Processes and Applications written by Yury A. Kutoyants and published by Springer Nature. This book was released on 2023-09-04 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers an extensive class of models involving inhomogeneous Poisson processes and deals with their identification, i.e. the solution of certain estimation or hypothesis testing problems based on the given dataset. These processes are mathematically easy-to-handle and appear in numerous disciplines, including astronomy, biology, ecology, geology, seismology, medicine, physics, statistical mechanics, economics, image processing, forestry, telecommunications, insurance and finance, reliability, queuing theory, wireless networks, and localisation of sources. Beginning with the definitions and properties of some fundamental notions (stochastic integral, likelihood ratio, limit theorems, etc.), the book goes on to analyse a wide class of estimators for regular and singular statistical models. Special attention is paid to problems of change-point type, and in particular cusp-type change-point models, then the focus turns to the asymptotically efficient nonparametric estimation of the mean function, the intensity function, and of some functionals. Traditional hypothesis testing, including some goodness-of-fit tests, is also discussed. The theory is then applied to three classes of problems: misspecification in regularity (MiR),corresponding to situations where the chosen change-point model and that of the real data have different regularity; optical communication with phase and frequency modulation of periodic intensity functions; and localization of a radioactive (Poisson) source on the plane using K detectors. Each chapter concludes with a series of problems, and state-of-the-art references are provided, making the book invaluable to researchers and students working in areas which actively use inhomogeneous Poisson processes.
Download or read book Random Processes for Engineers written by Bruce Hajek and published by Cambridge University Press. This book was released on 2015-03-12 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include: • Calculus of random processes in linear systems • Kalman and Wiener filtering • Hidden Markov models for statistical inference • The estimation maximization (EM) algorithm • An introduction to martingales and concentration inequalities. Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly tested homework problems (half of which are solved in detail at the end of the book).
Download or read book Poisson Sampling written by Michael S. Williams and published by . This book was released on 1998 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The prevailing assumption, that for Poisson sampling the adjusted estimator "Y-hat a" is always substantially more efficient than the unadjusted estimator "Y-hat u" , is shown to be incorrect. Some well known theoretical results are applicable since "Y-hat a" is a ratio-of-means estimator and "Y-hat u" a simple unbiased estimator. We formalize an additional realistic situation for high-value timber estimation for which "Y-hat u" is more efficient. (Please note: equations are spelled out inside quotation marks. Please see PDF for symbols.)"
Download or read book Mixed Poisson Processes written by J Grandell and published by CRC Press. This book was released on 2020-10-29 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: To date, Mixed Poisson processes have been studied by scientists primarily interested in either insurance mathematics or point processes. Work in one area has often been carried out without knowledge of the other area. Mixed Poisson Processes is the first book to combine and concentrate on these two themes, and to distinguish between the notions of distributions and processes. The first part of the text gives special emphasis to the estimation of the underlying intensity, thinning, infinite divisibility, and reliability properties. The second part is, to a greater extent, based on Lundberg's thesis.
