Matrix-Exponential Distributions in Applied Probability. 1st ed. 2017

種類:

電子ブック

責任表示:

by Mogens Bladt, Bo Friis Nielsen

出版情報:

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

著者名:

• Bladt, Mogens.
• Nielsen, Bo Friis.
• SpringerLink (Online service)

シリーズ名:

Probability Theory and Stochastic Modelling ; 81

ISBN:

9781493970490 [1493970496]    

注記:

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.
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 distribu

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