Matching Three Moments with Minimal Acyclic Phase Type Distributions

Bobbio, A.; Horváth, András; Telek, Miklós

doi:10.1081/stm-200056210

Cited by 141 publications

(121 citation statements)

References 7 publications

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“…It is guaranteed that, with appropriately large order, this procedure is able to match any set of 2N −1 moments belonging to a positive distribution. The other method operating on a flexible structure has been published in [2]. It matches 3 moments with an exponential and an Erlang distribution connected after each other in a row.…”

Section: Ph Distribution Fitting Based On Moment Matchingmentioning

confidence: 99%

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Moment Matching-Based Distribution Fitting with Generalized Hyper-Erlang Distributions

Horváth

2013

Analytical and Stochastic Modeling Techniques and Applications

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Abstract. This paper describes a novel moment matching based fitting method for phase-type (PH) distributions. A special sub-class of phase-type distributions is introduced for the fitting, called generalized hyper-Erlang distributions. The user has to provide only two parameters: the number of moments to match, and the upper bound for the sum of the multiplicities of the eigenvalues of the distribution, which is related to the maximal size of the resulting PH distribution. Given these two parameters, our method obtains all PH distributions that match the target moments and have a Markovian representation up to the given size. From this set of PH distributions the best one can be selected according to any distance function.

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Section: Ph Distribution Fitting Based On Moment Matchingmentioning

confidence: 99%

“…Moment matching with a mixture of Erlang distributions of common order (MECO, [11]); 4. The method of [2], which is able to match the first three moments only.…”

Section: Optimizing the R I Parametersmentioning

confidence: 99%

Moment Matching-Based Distribution Fitting with Generalized Hyper-Erlang Distributions

Horváth

2013

Analytical and Stochastic Modeling Techniques and Applications

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“…Closed form symbolical bounds for the second and third normalized moments of APH(n) distributions are published in [7]. The moment formulas of PH (3) distributions are much more complex than the ones of the APH(3).…”

Section: Moments Bounds Of the Ph(3) Classmentioning

confidence: 99%

“…The bounds for n 3 are provided by [7] for the APH(3) class, depicted in Figure 5. Two sets can be distinguished according to the figure, n 3 is lower and upper bounded in the first one (corresponding to 4/3 ≤ n 2 < 3/2, called SET-1 in the sequel), while it is only lower bounded in the second (where n 2 > 3/2, called SET-2 in the sequel).…”

Section: Bounds Of the Third Normalized Momentmentioning

confidence: 99%

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On the canonical representation of phase type distributions

Horváth

Telek

2009

Performance Evaluation

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The characterization and the canonical representation of order-n phase type distributions (PH(n)) is an open research problem.This problem is solved for n = 2, since the equivalence of the acyclic and the general PH distributions has been proven for a long time. However, no canonical representations have been introduced for the general PH distribution class so far for n > 2. In this paper we summarize the related results for n = 3. Starting from these results we provide a canonical representation of the PH(3) class (that is a minimal representation, too) and present a symbolical transformation procedure to obtain the canonical representation based on any (not only Markovian) vectormatrix representation of the distribution. We show that -using the same approachno symbolical results can be derived for the order-4 PH distributions, thus probably the PH(3) class is the highest order PH class for which a symbolical canonical transformation exists.Using the transformation method to canonical form for PH(3) we numerically evaluate the moment bounds of the PH(3) distribution set, compare it to the order-3 acyclic PH distribution (APH(3)) class, and present other possible applications of the canonical form.Email address: {ghorvath,telek}@hit.bme.hu (Gábor Horváth and Miklós Telek).

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2013

Markov Chains

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Matching Three Moments with Minimal Acyclic Phase Type Distributions

Cited by 141 publications

References 7 publications

Moment Matching-Based Distribution Fitting with Generalized Hyper-Erlang Distributions

Moment Matching-Based Distribution Fitting with Generalized Hyper-Erlang Distributions

On the canonical representation of phase type distributions

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