Point Processes With Order Statistic Property Mixtures Of Poisson Processes And Mixtures Of Linear Death Processes
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Point Processes with a Generalized Order Statistic Property
Author | : Birgit Debrabant |
Publisher | : Logos Verlag Berlin GmbH |
Total Pages | : 154 |
Release | : 2008 |
Genre | : |
ISBN | : 3832519599 |
Mixed Poisson processes are a well known class of point processes derived from (stationary) Poisson processes. In particular they cover cases where the intensity of a Poisson process is unknown but can be assumed to follow a known probability distribution. This situation is common e. g. in insurance mathematics where for instance the number of accident claims in which an individual is involved and which is evolving over some time can in principal be well described by a Poisson process with an individual, yet normally unknown intensity corresponding to the individual's accident proneness. Modelling this intensity as a random variable naturally leads to a mixed model. Usually, an insurance company will have a good estimate of the associated mixing distribution due to its large portfolio of policies.
Point Processes
Author | : D.R. Cox |
Publisher | : Routledge |
Total Pages | : 171 |
Release | : 2018-12-19 |
Genre | : Mathematics |
ISBN | : 1351423851 |
There has been much recent research on the theory of point processes, i.e., on random systems consisting of point events occurring in space or time. Applications range from emissions from a radioactive source, occurrences of accidents or machine breakdowns, or of electrical impluses along nerve fibres, to repetitive point events in an individual's medical or social history. Sometimes the point events occur in space rather than time and the application here raneg from statistical physics to geography. The object of this book is to develop the applied mathemathics of point processes at a level which will make the ideas accessible both to the research worker and the postgraduate student in probability and statistics and also to the mathemathically inclined individual in another field interested in using ideas and results. A thorough knowledge of the key notions of elementary probability theory is required to understand the book, but specialised "pure mathematical" coniderations have been avoided.
Point Process Models with Applications to Safety and Reliability
Author | : W. Thompson |
Publisher | : Springer Science & Business Media |
Total Pages | : 152 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 1461310679 |
In teaching an elementary course in stochastic processes it was noticed that many seemingly deep results in point processes are readily accessible by the device of representing them in terms of random gap lengths between points. The possibility of representing point processes in terms of sequences of random variables rather than probability measures makes them mathemati cally simpler than general stochastic processes. Point processes can be studied using only the tools of elementary probability, that is the joint distributions of finitely many random variables. Given the wide applicability of point process models and the difficulty of access by the measure-theoretic route, it was determined that the simpler representation is of sufficient expository im portance to deserve emphasis. The present book is the result: it is specialized and short and therefore is called a monograph. In its development the material has been taught to several classes with pleasing results. Students have apparently understood theorems which by other methods appear difficult and deep. A few of the results, particularly on reliability, safety assessment and clustering, are original applied research. An alternative title for this monograph might be 'Point processes: What they are and what they are good for.
Bulletin - Institute of Mathematical Statistics
Author | : Institute of Mathematical Statistics |
Publisher | : |
Total Pages | : 740 |
Release | : 1979 |
Genre | : Mathematical statistics |
ISBN | : |
An Introduction to the Theory of Point Processes
Author | : D.J. Daley |
Publisher | : Springer Science & Business Media |
Total Pages | : 487 |
Release | : 2006-04-10 |
Genre | : Mathematics |
ISBN | : 0387215646 |
Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.
Mixed Poisson Processes
Author | : J Grandell |
Publisher | : CRC Press |
Total Pages | : 284 |
Release | : 2020-10-29 |
Genre | : Mathematics |
ISBN | : 1000153037 |
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.
Point Process Theory and Applications
Author | : Martin Jacobsen |
Publisher | : Springer Science & Business Media |
Total Pages | : 325 |
Release | : 2006-07-27 |
Genre | : Mathematics |
ISBN | : 0817644636 |
Mathematically rigorous exposition of the basic theory of marked point processes and piecewise deterministic stochastic processes Point processes are constructed from scratch with detailed proofs Includes applications with examples and exercises in survival analysis, branching processes, ruin probabilities, sports (soccer), finance and risk management, and queueing theory Accessible to a wider cross-disciplinary audience
Random Point Processes
Author | : Donald Lee Snyder |
Publisher | : Wiley-Interscience |
Total Pages | : 504 |
Release | : 1975 |
Genre | : Mathematics |
ISBN | : |
An Introduction to the Theory of Point Processes
Author | : Daryl J. Daley |
Publisher | : Springer Science & Business Media |
Total Pages | : 720 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 1475720017 |
Stochastic point processes are sets of randomly located points in time, on the plane or in some general space. This book provides a general introduction to the theory, starting with simple examples and an historical overview, and proceeding to the general theory. It thoroughly covers recent work in a broad historical perspective in an attempt to provide a wider audience with insights into recent theoretical developments. It contains numerous examples and exercises. This book aims to bridge the gap between informal treatments concerned with applications and highly abstract theoretical treatments.