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Probability Theory and Stochastic Modelling

Matrix-Exponential Distributions in Applied Probability

Authors: Bladt, Mogens, Nielsen, Bo Friis

  • Only book that treats the theory of matrix-exponential distributions comprehensively
  • Students will benefit from obtaining general tools which may be applied in a variety of situations.
  • The matrix—exponential methodology allows for calculating quantities in advanced stochastic models explicitly 
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Buy this book

eBook $74.99
price for USA (gross)
  • ISBN 978-1-4939-7049-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-1-4939-7047-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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 on 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.

About the authors

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).

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Table of contents (13 chapters)

  • Preliminaries on Stochastic Processes

    Bladt, Mogens (et al.)

    Pages 1-71

  • Martingales and More General Markov Processes

    Bladt, Mogens (et al.)

    Pages 73-124

  • Phase-Type Distributions

    Bladt, Mogens (et al.)

    Pages 125-197

  • Matrix-Exponential Distributions

    Bladt, Mogens (et al.)

    Pages 199-296

  • Renewal Theory

    Bladt, Mogens (et al.)

    Pages 297-359

Buy this book

eBook $74.99
price for USA (gross)
  • ISBN 978-1-4939-7049-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-1-4939-7047-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Matrix-Exponential Distributions in Applied Probability
Authors
Series Title
Probability Theory and Stochastic Modelling
Series Volume
81
Copyright
2017
Publisher
Springer US
Copyright Holder
Springer Science+Business Media LLC
eBook ISBN
978-1-4939-7049-0
DOI
10.1007/978-1-4939-7049-0
Hardcover ISBN
978-1-4939-7047-6
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XVII, 736
Number of Illustrations and Tables
37 b/w illustrations, 21 illustrations in colour
Topics