國立虎尾科技大學 |

Matrix-Exponential Distributions in Applied Probability

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Matrix-Exponential Distributions in Applied Probability/ by Mogens Bladt, Bo Friis Nielsen.
作者:	Bladt, Mogens.
其他作者:	Nielsen, Bo Friis.
出版者:	Boston, MA :Springer US : : 2017.,
面頁冊數:	xvii, 736 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Markov processes. -
電子資源:	http://dx.doi.org/10.1007/978-1-4939-7049-0
ISBN:	9781493970490

Matrix-Exponential Distributions in Applied Probability
Bladt, Mogens.

Matrix-Exponential Distributions in Applied Probability[electronic resource] /by Mogens Bladt, Bo Friis Nielsen. - Boston, MA :Springer US :2017. - xvii, 736 p. :ill. (some col.), digital ;24 cm. - Probability theory and stochastic modelling,v.812199-3130 ;. - Probability theory and stochastic modelling ;v.72..

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 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.

ISBN: 9781493970490

Standard No.: 10.1007/978-1-4939-7049-0doiSubjects--Topical Terms:

527825
Markov processes.

LC Class. No.: QA274.7

Dewey Class. No.: 519.233

Matrix-Exponential Distributions in Applied Probability
LDR:03134nam a2200337 a 4500 001 885515
003 DE-He213
005 20170518204506.0
006 m d
007 cr nn 008maaau
008 180530s2017 mau s 0 eng d
020 $a 9781493970490 $q (electronic bk.)
020 $a 9781493970476 $q (paper)
024 7 $a 10.1007/978-1-4939-7049-0 $2 doi
035 $a 978-1-4939-7049-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274.7
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
082 0 4 $a 519.233 $2 23
090 $a QA274.7 $b .B632 2017
100 1 $a Bladt, Mogens. $3 1142743
245 1 0 $a Matrix-Exponential Distributions in Applied Probability $h [electronic resource] / $c by Mogens Bladt, Bo Friis Nielsen.
260 $a Boston, MA : $c 2017. $b Springer US : $b Imprint: Springer,
300 $a xvii, 736 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Probability theory and stochastic modelling, $x 2199-3130 ; $v v.81
505 0 $a 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.
520 $a 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.
650 0 $a Markov processes. $3 527825
650 0 $a Probabilities. $3 527847
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Operations Research, Management Science. $3 785065
700 1 $a Nielsen, Bo Friis. $3 1142744
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Probability theory and stochastic modelling ; $v v.72. $3 1064457
856 4 0 $u http://dx.doi.org/10.1007/978-1-4939-7049-0
950 $a Mathematics and Statistics (Springer-11649)