Results 261 to 270 of about 15,413,531 (300)

Bilateral Phase Type Distributions

Stochastic Models, 2005
Abstract A new class of probability distributions called “bilateral phase type distributions (BPH)” on (−∞, ∞) is defined as a generalization of the versatile class of phase type (PH) distributions on [0, ∞) introduced by Marcel F. Neuts. We derive the basic descriptors of such distributions in an algorithmically tractable manner and show that this ...
Soohan Ahn, V. Ramaswami
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Estimation of Phase-Type Distributions

2017
This chapter deals with the estimation of phase-type distributions in a number of different circumstances. First, we consider their estimation when only absorption times are available, and provide both EM and MCMC approaches, which in turn complement each other, aiming at different purposes. Then we consider censored data of a different kind, which can
Mogens Bladt, Bo Friis Nielsen
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A New Class of Multivariate Phase Type Distributions

Operations Research, 1989
A new class of multivariate phase type distributions (denoted by MPH*) is defined, based upon the total accumulated reward until absorption in a finite state, continuous time Markov chain. This new class is shown to be a strict superset of the class of multivariate phase type distributions MPH introduced by Assaf, Langberg, Savits and Shaked.
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Moment distributions of phase-type (abstract only)

ACM SIGMETRICS Performance Evaluation Review, 2012
Both matrix-exponential and phase-type distributions have a number of important closure properties. Among those are the distributions of the age and residual life-time of a stationary renewal process with inter-arrivals of either type. In this talk we show that the spread, which is the sum of the age an residual life-time, is also phase-type ...
Mogens Bladt, Bo Friis Nielsen
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Characterization of phase-type distributions

Communications in Statistics. Stochastic Models, 1990
A distribution with rational Laplace-Stieltjes transform is of phase type if and only if it is either the point mass at zero, or it has a continuous positive density on the positive reals and its Laplace-Stieltjes transform has a unique pole of maximal real part (which is therefore real). This result is proved, and the corresponding characterization of
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Lévy Processes, Phase-Type Distributions, and Martingales

Stochastic Models, 2014
Levy processes are defined as processes with stationary independent increments and have become increasingly popular as models in queueing, finance, etc.; apart from Brownian motion and compound Poisson processes, some popular examples are stable processes, variance gamma processes, CGMY Levy processes (tempered stable processes), NIG (normal inverse ...
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PHASE: A Stochastic Formalism for Phase-Type Distributions

2014
Models of non-Markovian systems expressed using stochastic formalisms often employ phase-type distributions in order to approximate the duration of transitions. We introduce a stochastic process calculus named PHASE which operates with phase-type distributions, and provide a step-by-step description of how PHASE processes can be translated into models ...
Gabriel Ciobanu, Armand Stefan Rotaru
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Modelling healthcare systems with phase-type distributions

Health Care Management Science, 2008
Phase-type distributions constitute a very versatile class of distributions. They have been used in a wide range of stochastic modelling applications in areas as diverse as telecommunications, finance, biostatistics, queueing theory, drug kinetics, and survival analysis.
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Examples of fitting structured phase–type distributions

Applied Stochastic Models and Data Analysis, 1994
AbstractA sub–class of phase–type distributions is defined in terms of a Markov process with sequential transitions between transient states and transitions from these states to absorption. Such distributions form a very rich class; they can be fitted to data, and any structure revealed by the parameter estimates used to develop more parsimonious re ...
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From the Exponential Distribution to Phase-Type Distributions

2013
This chapter introduces phase-type distributions. Topics covered in this chapter are: (i) the exponential distribution; (ii) definitions of phase-type distributions; (iii) closure properties of phase-type distributions; (iv) PH-representations; (v) multivariate phase-type distributions; and (vi) parameter estimation and fitting of phase-type ...
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