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Titlebook: Matrix-Exponential Distributions in Applied Probability; Mogens Bladt,Bo Friis Nielsen Textbook 2017 Springer Science+Business Media LLC 2

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发表于 2025-3-21 18:37:08 | 显示全部楼层 |阅读模式
书目名称Matrix-Exponential Distributions in Applied Probability
编辑Mogens Bladt,Bo Friis Nielsen
视频video
概述Only book that treats the theory of matrix-exponential distributions comprehensively.Students will benefit from obtaining general tools which may be applied in a variety of situations..The matrix—expo
丛书名称Probability Theory and Stochastic Modelling
图书封面Titlebook: Matrix-Exponential Distributions in Applied Probability;  Mogens Bladt,Bo Friis Nielsen Textbook 2017 Springer Science+Business Media LLC 2
描述.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 treatmenton 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, t
出版日期Textbook 2017
关键词Applied probability; Markov Processes; Matrix--exponential distributions; Numerical methods; Stochastic
版次1
doihttps://doi.org/10.1007/978-1-4939-7049-0
isbn_softcover978-1-4939-8377-3
isbn_ebook978-1-4939-7049-0Series ISSN 2199-3130 Series E-ISSN 2199-3149
issn_series 2199-3130
copyrightSpringer Science+Business Media LLC 2017
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发表于 2025-3-21 23:42:31 | 显示全部楼层
Mogens Bladt,Bo Friis Nielsent some new results concerning the distribution problem together with a computation method, the Cartesian Integration Method (CIM), which seems effective for practical problems, if the number of random factors taken into account is not too large. although all the coefficients may be random.
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Mogens Bladt,Bo Friis Nielsenz. T. noch einer exakten mathematischen Form bedürfen. Hieraus können sich fruchtbare Impulse sowohl für theoretische Untersuchungen als auch für die eng mit der Praxis verbundene wissenschaftliche Tätigkeit ergeben. Die 49 Teilnehmer, darunter aus Rumänien, Großbritannien, den USA, der Schweiz, den
发表于 2025-3-22 15:36:51 | 显示全部楼层
Mogens Bladt,Bo Friis Nielsen increasing accuracy as these degrees increase. The approximations are examples of a more general situation where a function f to be approximated is split in two parts f = f. + f., with f. as a simple “preconditioning” part, which mainly serves to give the “accuracy” part f. certain desirable qualit
发表于 2025-3-22 20:13:51 | 显示全部楼层
Some Applications to Risk Theory, and Sparre–Andersen models, but with the linear increments between claims replaced by a Brownian motion with a corresponding drift. The last model considers the calculation of the probability of ruin in finite time. The method is algorithmic and uses a so-called Erlangization scheme.
发表于 2025-3-22 22:51:05 | 显示全部楼层
Estimation of Phase-Type Distributions,discretely observed phase-type distributions. As a byproduct, we also obtain a general method for estimating discretely observed Markov jump processes, which can be of interest on its own. Finally, the EM algorithm can be extended to approximate a given theoretical distribution by seeing it as empir
发表于 2025-3-23 03:36:56 | 显示全部楼层
Textbook 2017sk. We emphasize our intention towards applications by including an extensive treatmenton 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, t
发表于 2025-3-23 08:20:20 | 显示全部楼层
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