Statistical Inference for Periodic and Partially Observable Poisson Processes PDF Download
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Author: Ferdian Jovan
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Ferdian Jovan
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Yury A. Kutoyants
Publisher: Springer Nature
ISBN: 3031370546
Category : Mathematics
Languages : en
Pages : 683
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Book Description
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.
Author: Yi Lu
Publisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 0
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Book Description
Periodic non-homogeneous Poisson processes and Poisson models under Markovian environments are studied in this thesis. By accounting for periodic seasonal variations and random fluctuations in the underlying risk, these models generalize the classical homogeneous Poison risk model. Non-homogenous Poisson processes with periodic claim intensity rates are proposed for the claim counting process of risk theory. We introduce a doubly periodic Poisson model with short and long-term trends. Beta-type intensity functions are presented as illustrations. Doubly periodic Poisson models are appropriate when the seasonality does not repeat the exact same short-term pattern every year, but has a peak intensity that varies over a longer period. This reflects periodic environments like those forming hurricanes, in alternating El Niño/La Niña years. The properties of the model and the statistical inference of the model parameters are discussed. An application of the model to the dataset of Atlantic Hurricanes Affecting the United States (1899-2000) is discussed in detail. Further we introduce a periodic regime-switching Cox risk model by considering both, seasonal variations and stochastic fluctuations in the claims intensity. The intensity process, governed by a periodic function with a random peak level, is proposed. The periodic intensity function follows a deterministic pattern in each short-term period, and is illustrated by a beta-type function. A finite-state Markov chain defines the level process, explaining the random effect due to different underlying risk years. The properties of this regime-switching claim counting process are discussed in detail. By properly defining the Lundberg coefficient; Lundberg-type bounds for finite time ruin probabilities in the two-state risk model case are derived. A detailed derivation of the likelihood function and the maximum likelihood estimates of the model parameters is also given. Statistical applications of the model to the Atlantic hurricanes affecting the United States dataset are discussed under two different level classifications schemes. The Markov-modulated risk model is considered to reflect a risk process or insurance business alternating between a finite number of Poisson models. Here we assume that the claim inter-arrivals, claim severities and premiums of the model are influenced by an external Markovian environment. The effect of this external environment may be characterized, at any time, by a state variable, representing for example, certain types of epidemics, a variety of weather conditions or of different states of the economy.
Author: J Grandell
Publisher: CRC Press
ISBN: 1000109992
Category : Mathematics
Languages : en
Pages : 281
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Book Description
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.
Author: Charles Jacob MacLean
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 242
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Author: J. F. C. Kingman
Publisher: Clarendon Press
ISBN: 0191591246
Category : Mathematics
Languages : en
Pages : 118
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Book Description
In the theory of random processes there are two that are fundamental, and occur over and over again, often in surprising ways. There is a real sense in which the deepest results are concerned with their interplay. One, the Bachelier Wiener model of Brownian motion, has been the subject of many books. The other, the Poisson process, seems at first sight humbler and less worthy of study in its own right. Nearly every book mentions it, but most hurry past to more general point processes or Markov chains. This comparative neglect is ill judged, and stems from a lack of perception of the real importance of the Poisson process. This distortion partly comes about from a restriction to one dimension, while the theory becomes more natural in more general context. This book attempts to redress the balance. It records Kingman's fascination with the beauty and wide applicability of Poisson processes in one or more dimensions. The mathematical theory is powerful, and a few key results often produce surprising consequences.
Author: Frank A. Haight
Publisher:
ISBN:
Category : Poisson distribution
Languages : en
Pages : 192
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Author: Tomasz Rolski
Publisher:
ISBN:
Category :
Languages : en
Pages : 58
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Author: Magdy Sayed Khedr
Publisher:
ISBN:
Category :
Languages : en
Pages : 246
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Author: John Frank Charles Kingman
Publisher:
ISBN:
Category : Poisson process
Languages : en
Pages : 104
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Book Description
On the poisson process
