Matrix-Exponential Distributions in Applied Probability

Business & Finance, Management & Leadership, Operations Research, Nonfiction, Science & Nature, Mathematics, Statistics
Cover of the book Matrix-Exponential Distributions in Applied Probability by Mogens Bladt, Bo Friis Nielsen, Springer US
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Mogens Bladt, Bo Friis Nielsen ISBN: 9781493970490
Publisher: Springer US Publication: May 18, 2017
Imprint: Springer Language: English
Author: Mogens Bladt, Bo Friis Nielsen
ISBN: 9781493970490
Publisher: Springer US
Publication: May 18, 2017
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer US

Cover of the book Biomedical Institutions, Biomedical Funding, and Public Policy by Mogens Bladt, Bo Friis Nielsen
Cover of the book Biomedical Ethics and the Law by Mogens Bladt, Bo Friis Nielsen
Cover of the book Infections of the Gastrointestinal Tract by Mogens Bladt, Bo Friis Nielsen
Cover of the book Lymph Node Cytopathology by Mogens Bladt, Bo Friis Nielsen
Cover of the book Hybrid Finite Element Method for Stress Analysis of Laminated Composites by Mogens Bladt, Bo Friis Nielsen
Cover of the book Handbook of Risk Management in Energy Production and Trading by Mogens Bladt, Bo Friis Nielsen
Cover of the book Electron-Diffraction Analysis of Clay Mineral Structures by Mogens Bladt, Bo Friis Nielsen
Cover of the book Cancer Chemotherapy: Concepts, Clinical Investigations and Therapeutic Advances by Mogens Bladt, Bo Friis Nielsen
Cover of the book Sports Data Mining by Mogens Bladt, Bo Friis Nielsen
Cover of the book Alternative and Complementary Therapies for Cancer by Mogens Bladt, Bo Friis Nielsen
Cover of the book Visual Development by Mogens Bladt, Bo Friis Nielsen
Cover of the book The New Dimensions of Warfarin Prophylaxis by Mogens Bladt, Bo Friis Nielsen
Cover of the book Blood Oxygenation by Mogens Bladt, Bo Friis Nielsen
Cover of the book Mycotoxins in Foodstuffs by Mogens Bladt, Bo Friis Nielsen
Cover of the book The Design of Low-Voltage, Low-Power Sigma-Delta Modulators by Mogens Bladt, Bo Friis Nielsen
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy