Results 271 to 280 of about 287,761 (311)

Approximation of Discrete Phase-Type Distributions

38th Annual Simulation Symposium, 2005
The analysis of discrete stochastic models such as generally distributed stochastic Petri nets can be done using state space-based methods. The behavior of the model is described by a Markov chain that can be solved mathematically. The phase-type distributions that are used to describe non-Markovian distributions have to be approximated.
Claudia Isensee, Graham Horton
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Phase-Type Distributions

2017
The class of distributions on [0, ∞) having a rational Laplace transform (i.e., a Laplace transform that is the fraction between two polynomials) will, for reasons that will become apparent in the next chapter, be referred to as matrix-exponential distributions.
Mogens Bladt, Bo Friis Nielsen
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Phase-Type Distributions

2014
Continuous-time Markov chainsContinuous-time Markov chain (CTMCs)CTMC seealso Continuous-time Markov chain Markov chain seealso Continuous-time Markov chain are a class of stochastic processes with a discrete state space in which the time between transitions follows an exponential distribution.
Peter Buchholz, Jan Kriege, Iryna Felko
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Multivariate finite-support phase-type distributions

Journal of Applied Probability, 2020
AbstractWe introduce a multivariate class of distributions with support I, a k-orthotope in $[0,\infty)^{k}$ , which is dense in the set of all k-dimensional distributions with support I. We call this new class ‘multivariate finite-support phase-type distributions’ (MFSPH). Though we generally define MFSPH distributions on any finite k-orthotope in $[
Celeste R. Pavithra, T. G. Deepak
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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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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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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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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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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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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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