Estimation in Mixed Poisson Process Models PDF Download
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Author: Etsuo Miyaoka
Publisher:
ISBN:
Category :
Languages : en
Pages : 240
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Book Description
Author: Etsuo Miyaoka
Publisher:
ISBN:
Category :
Languages : en
Pages : 240
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Book Description
Author: J Grandell
Publisher: CRC Press
ISBN: 1000153037
Category : Mathematics
Languages : en
Pages : 284
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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: Remy Julius Van de Ven
Publisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 344
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Book Description
Author: Vladimir E. Bening
Publisher: VSP
ISBN: 9789067643665
Category : Science
Languages : en
Pages : 464
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Book Description
This volume in the "Modern Probability and Statistics series aims to fill the gap in existing literature on compound Cox processes, i.e. sums of independent identically distributed random variables up to a doubly stochastic Poisson process, which are very important, especially for insurance and financial applications where they provide good asymptotic approximations for basic characteristics such as the distributions of the surplus of an insurance company under risk and portfolio fluctuations or of increments of stock prices under non-constant intensity of trade. It presents the present state-of-the-art in the field of compound Cox processes and their applications in insurance and finance. Besides a review of well-known classical results on compound and mixed Poisson processes and risk theory, it contains many new, recently obtained results by the authors. Among these are: new convergence criteria, convergence rate estimates, asymptotic expansions for quantiles of stochastic processes and many others. From the applied problems considered in this book, four deserve to be mentioned especially: 1) modelling the distribution of increments of stock prices, closely connected with prediction of the behaviour of financial indexes; 2) the description of asymptotic behaviour of the so-called generalized risk processes, which take into account both risk and portfolio fluctuations; 3) statistical estimation of the probability of ruin for a generalized risk process; 4) construction of refined approximations to the ruin probability, based on its asymptotic expansions with small safety loading. This book will be of great value to specialists in applied probability and to those who use modelsand methods of probability theory to solve practical problems in the fields of insurance and finance.
Author: Mina Habibi
Publisher:
ISBN:
Category : Multiscalemodeling
Languages : en
Pages : 13
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Book Description
In this article, a new mixed Poisson distribution that includes the geometric and negative binomial distributions as special cases is proposed. This distribution is obtained by mixing the Poisson distribution with the binomial exponential 2 distribution. The new distribution is overdispersed (i.e., the variance is greater than the mean), and hence, this distribution is able to incorporate the overdispersion that typically occurs in count data sets. Shape and moments properties of the proposed distribution are discussed. Estimation of the model parameters is considered using the method of moments and maximum likelihood approach. We propose an algorithm for generating random data from the new distribution. Three real data applications are also presented to see that new distribution is useful for modeling count data.
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: Frank A. Haight
Publisher:
ISBN:
Category : Poisson distribution
Languages : en
Pages : 192
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Book Description
Author: Paul Roback
Publisher: CRC Press
ISBN: 1439885400
Category : Mathematics
Languages : en
Pages : 436
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Book Description
Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R is designed for undergraduate students who have successfully completed a multiple linear regression course, helping them develop an expanded modeling toolkit that includes non-normal responses and correlated structure. Even though there is no mathematical prerequisite, the authors still introduce fairly sophisticated topics such as likelihood theory, zero-inflated Poisson, and parametric bootstrapping in an intuitive and applied manner. The case studies and exercises feature real data and real research questions; thus, most of the data in the textbook comes from collaborative research conducted by the authors and their students, or from student projects. Every chapter features a variety of conceptual exercises, guided exercises, and open-ended exercises using real data. After working through this material, students will develop an expanded toolkit and a greater appreciation for the wider world of data and statistical modeling. A solutions manual for all exercises is available to qualified instructors at the book’s website at www.routledge.com, and data sets and Rmd files for all case studies and exercises are available at the authors’ GitHub repo (https://github.com/proback/BeyondMLR)
Author: Rainer Winkelmann
Publisher: Springer Science & Business Media
ISBN: 354078389X
Category : Business & Economics
Languages : en
Pages : 342
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Book Description
The book provides an up-to-date survey of statistical and econometric techniques for the analysis of count data, with a focus on conditional distribution models. The book starts with a presentation of the benchmark Poisson regression model. Alternative models address unobserved heterogeneity, state dependence, selectivity, endogeneity, underreporting, and clustered sampling. Testing and estimation is discussed. Finally, applications are reviewed in various fields.
Author: Kathryn Jo-Anne Barger
Publisher:
ISBN:
Category :
Languages : en
Pages : 228
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Book Description
