Access the full text.
Sign up today, get DeepDyve free for 14 days.
C. McGrory, A. Pettitt, M. Faddy (2009)
A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent meanComput. Stat. Data Anal., 53
H. Okamura, T. Dohi, Kishor Trivedi (2009)
Markovian Arrival Process Parameter Estimation With Group DataIEEE/ACM Transactions on Networking, 17
A. Panchenko, Axel Thümmler (2007)
Efficient phase-type fitting with aggregated traffic tracesPerform. Evaluation, 64
Author Wu, F. BYC., WU Jeff (1983)
ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHMAnnals of Statistics, 11
Marita Olsson (1993)
Estimation of phase type distributions from censored samplesScandinavian Journal of Statistics, 23
Ren Asmussen, O. Nerman, Marita Olsson (1996)
Fitting Phase-type Distributions via the EM AlgorithmScandinavian Journal of Statistics, 23
A. Cumani (1982)
On the canonical representation of homogeneous markov processes modelling failure - time distributionsMicroelectronics Reliability, 22
Mary Johnson, M. Taaffe (1989)
Matching moments to phase distri-butions: mixtures of Erlang distribution of common order
T. Osogami, Mor Harchol-Balter (2006)
Closed form solutions for mapping general distributions to quasi-minimal PH distributionsPerform. Evaluation, 63
D. Scott (1979)
On optimal and data based histogramsBiometrika, 66
A. Dempster, N. Laird, D. Rubin (1977)
Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper
M. Telek, G. Horváth (2007)
A minimal representation of Markov arrival processes and a moments matching methodPerform. Evaluation, 64
Olsson Olsson (1996)
Estimation of phase‐type distributions from censored dataScandinavian Journal of Statistics, 23
M. Heijden (1988)
On the Three-Moment Approximation of a General Distribution by a Coxian DistributionProbability in the Engineering and Informational Sciences, 2
Peter Bosch, D. Dietz, E. Pohl (2000)
Moment matching using a family of phase-type distributionsCommunications in Statistics. Stochastic Models, 16
H. Okamura, T. Dohi, Kishor Trivedi (2011)
A refined EM algorithm for PH distributionsPerform. Evaluation, 68
M. Ausín, Michael Wiper, R. Lillo (2008)
Bayesian prediction of the transient behaviour and busy period in short- and long-tailed GI/G/1 queueing systemsComput. Stat. Data Anal., 52
Axel Thümmler, P. Buchholz, M. Telek (2006)
A Novel Approach for Phase-Type Fitting with the EM AlgorithmIEEE Transactions on Dependable and Secure Computing, 3
M. Ausín, Michael Wiper, R. Lillo (2004)
Bayesian estimation for the M/G/1 queue using a phase-type approximationJournal of Statistical Planning and Inference, 118
Telek (2002)
Matching moments for acyclic discrete and continuous phase-type distributions of second orderInt'l Journal of Simulation Systems, Science & Technology, 3
M. Johnson, M. Taaffe (1990)
Matching moments to phase distributions: density function shapesStochastic Models, 6
H. Okamura, T. Dohi (2009)
Faster Maximum Likelihood Estimation Algorithms for Markovian Arrival Processes2009 Sixth International Conference on the Quantitative Evaluation of Systems
Geoffrey McLachlan, P. Jones (1988)
Fitting mixture models to grouped and truncated data via the EM algorithm.Biometrics, 44 2
A. Reibman, Kishor Trivedi (1988)
Numerical transient analysis of markov modelsComput. Oper. Res., 15
A. Bobbio, M. Telek (1994)
A benchmark for ph estimation algorithms: results for acyclic-phStochastic Models, 10
Dempster Dempster, Laird Laird, Rubin Rubin (1977)
Maximum likelihood from incomplete data via the EM algorithmJournal of the Royal Statistical Society, Series B, 39
Qi-Ming He, Hanqin Zhang (2008)
An Algorithm for Computing Minimal % Coxian RepresentationsINFORMS J. Comput., 20
M. Malhotra, K. Muppala, Kishor Trivedi (1994)
STIFFNESS-TOLERANT METHODS FOR TRANSIENT ANALYSIS OF STIFF MARKOV CHAINSMicroelectronics Reliability, 34
L. Hansen (1982)
Large Sample Properties of Generalized Method of Moments EstimatorsEconometrica, 50
A. Bobbio, A. Horváth, M. Scarpa, M. Telek (2003)
Acyclic discrete phase type distributions: properties and a parameter estimation algorithmPerform. Evaluation, 54
M. Johnson (1993)
Selecting Parameters of Phase Distributions: Combining Nonlinear Programming, Heuristics, and Erlang DistributionsINFORMS J. Comput., 5
Andrea Bobbio, András Horváth, M. Telek (2005)
Matching Three Moments with Minimal Acyclic Phase Type DistributionsStochastic Models, 21
M. Bladt, A. González, S. Lauritzen (2003)
The estimation of phase-type related functionals using Markov chain Monte Carlo methodsScandinavian Actuarial Journal, 2003
This paper proposes an improved expectation–maximization (EM) algorithm for phase‐type (PH) distributions with grouped and truncated data. Olsson (1996) derived an EM algorithm for PH distributions under censored data, and the similar technique can be utilized to the PH fitting even under grouped and truncated data. However, it should be noted that Olsson's algorithm has a drawback in terms of computation speed. Because the time complexity of the algorithm is a cube of number of phases, it does not work well in the case where the number of phases is large. This paper proposes an improvement of the EM algorithm under grouped and truncated observations. By applying a uniformization‐based technique for continuous‐time Markov chains, it is shown that the time complexity of our algorithm can be reduced to the square of number of phases. In particular, when we consider the PH fitting using a canonical form of PH distributions, the time complexity is linear in the number of phases. Copyright © 2012 John Wiley & Sons, Ltd.
Applied Stochastic Models in Business and Industry – Wiley
Published: Mar 1, 2013
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.