Matrix-Exponential Distributions in Applied Probability

• Main Authors: Bladt, Mogens (Author), Nielsen, Bo Friis (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Springer US : Imprint: Springer, 2017.
• Series: Probability Theory and Stochastic Modelling, 81
• Subjects: Mathematics.; Operations research.; Management science.; Probabilities.; Probability Theory and Stochastic Processes.; Operations Research, Management Science.

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...

Table of 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.