Matrix-Exponential Distributions in Applied Probability

Mogens Bladt, Bo Friis Nielsen (Autoren)

Buch | Hardcover

736 Seiten

2017 | 1st ed. 2017
Springer-Verlag New York Inc.
978-1-4939-7047-6 (ISBN)

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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 treatmenton statistical 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.

Bo Friis Nielsen is an associate professor in the Department of Applied Mathematics and Computer Science at the Technical University of Denmark. Mogens Bladt is a researcher in the Department of Probability and Statistics at the Institute for Applied Mathematics and Systems, National University of Mexico (UNAM).

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.

Erscheinungsdatum	07.06.2017
Reihe/Serie	Probability Theory and Stochastic Modelling ; 81
Zusatzinfo	21 Illustrations, color; 37 Illustrations, black and white; XVII, 736 p. 58 illus., 21 illus. in color.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Themenwelt	Wirtschaft ► Betriebswirtschaft / Management
Schlagworte	Operations Research
ISBN-10	1-4939-7047-X / 149397047X
ISBN-13	978-1-4939-7047-6 / 9781493970476
Zustand	Neuware