Matrix-Exponential Distributions in Applied Probability / by Mogens Bladt, Bo Friis Nielsen.

Format:

Book

Author/Creator:

Bladt, Mogens., Author.

Nielsen, Bo Friis., Author.

Series:

Probability Theory and Stochastic Modelling, 2199-3130 ; 81

Language:

English

Subjects (All):

Probabilities.

Operations research.

Management science.

Probability Theory and Stochastic Processes.

Operations Research, Management Science.

Local Subjects:

Probability Theory and Stochastic Processes.

Operations Research, Management Science.

Physical Description:

1 online resource (XVII, 736 p. 58 illus., 21 illus. in color.)

Edition:

1st ed. 2017.

Place of Publication:

New York, NY : Springer US : Imprint: Springer, 2017.

Summary:

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. .

Contents:

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.

ISBN:

1-4939-7049-6