000 04115nam a22005175i 4500
001 978-1-4939-7049-0
003 DE-He213
005 20181204134416.0
007 cr nn 008mamaa
008 170518s2017 xxu| s |||| 0|eng d
020 _a9781493970490
_9978-1-4939-7049-0
024 7 _a10.1007/978-1-4939-7049-0
_2doi
040 _aISI Library, Kolkata
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aBladt, Mogens.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMatrix-Exponential Distributions in Applied Probability
_h[electronic resource] /
_cby Mogens Bladt, Bo Friis Nielsen.
264 1 _aBoston, MA :
_bSpringer US :
_bImprint: Springer,
_c2017.
300 _aXVII, 736 p. 58 illus., 21 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProbability Theory and Stochastic Modelling,
_x2199-3130 ;
_v81
505 0 _aPreface -- 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 _aThis 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 _aDistribution (Probability theory.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aOperations Research, Management Science.
_0http://scigraph.springernature.com/things/product-market-codes/M26024
700 1 _aNielsen, Bo Friis.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781493970476
776 0 8 _iPrinted edition:
_z9781493970483
776 0 8 _iPrinted edition:
_z9781493983773
830 0 _aProbability Theory and Stochastic Modelling,
_x2199-3130 ;
_v81
856 4 0 _uhttps://doi.org/10.1007/978-1-4939-7049-0
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c426978
_d426978