Matrix-Exponential Distributions in Applied Probability

Bo Friis Nielsen

ISBN 10: 149397047X / ISBN 13: 9781493970476

Verlag: Springer US, Springer US, 2017

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - 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.

Bestandsnummer des Verkäufers 9781493970476

Bibliografische Details

• Titel: Matrix-Exponential Distributions in Applied Probability
• Verlag: Springer US, Springer US
• Erscheinungsjahr: 2017
• Sprache: Englisch
• ISBN-10: 149397047X
• ISBN-13: 9781493970476
• Einband: Buch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

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).