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＜電子ブック＞
Matrix-Exponential Distributions in Applied Probability / by Mogens Bladt, Bo Friis Nielsen
(Probability Theory and Stochastic Modelling. ISSN:21993149 ; 81)

版	1st ed. 2017.
出版者	(New York, NY : Springer US : Imprint: Springer)
出版年	2017
本文言語	英語
大きさ	XVII, 736 p. 58 illus., 21 illus. in color : online resource
著者標目	*Bladt, Mogens author Nielsen, Bo Friis author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Operations research LCSH:Management science FREE:Probability Theory FREE:Operations Research, Management Science
一般注記	Preface -- Notation -- Preliminaries on Stochastic Processes -- Martingales and More General Markov Processes -- Phase-type Distributions -- Matrix-exponential Distributions -- Renewal Theory -- Random Walks -- Regeneration and Harris Chains -- Multivariate Distributions -- Markov Additive Processes -- Markovian Point Processes -- Some Applications to Risk Theory -- Statistical Methods for Markov Processes -- Estimation of Phase-type Distributions -- Bibliographic Notes -- Appendix This book contains an in-depth treatment of matrix-exponential (ME) distributions and their sub-class of phase-type (PH) distributions. Loosely speaking, an ME distribution is obtained through replacing the intensity parameter in an exponential distribution by a matrix. The ME distributions can also be identified as the class of non-negative distributions with rational Laplace transforms. If the matrix has the structure of a sub-intensity matrix for a Markov jump process we obtain a PH distribution which allows for nice probabilistic interpretations facilitating the derivation of exact solutions and closed form formulas. The full potential of ME and PH unfolds in their use in stochastic modelling. Several chapters on generic applications, like renewal theory, random walks and regenerative processes, are included together with some specific examples from queueing theory and insurance risk. We emphasize our intention towards applications by including an extensive treatment onstatistical methods for PH distributions and related processes that will allow practitioners to calibrate models to real data. Aimed as a textbook for graduate students in applied probability and statistics, the book provides all the necessary background on Poisson processes, Markov chains, jump processes, martingales and re-generative methods. It is our hope that the provided background may encourage researchers and practitioners from other fields, like biology, genetics and medicine, who wish to become acquainted with the matrix-exponential method and its applications. HTTP:URL=https://doi.org/10.1007/978-1-4939-7049-0

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