Bilateral matrix-exponential distributions

Mogens Bladt; Luz Judith R Esparza; Bo Friis Nielsen

doi:10.1145/2185395.2185405

Bilateral matrix-exponential distributions

Mogens Bladt, Luz Judith R Esparza, Bo Friis Nielsen

Research output: Contribution to journal › Conference abstract in journal › Research › peer-review

Abstract

In this article we define the classes of bilateral and multivariate bilateral matrix-exponential distributions. These distributions have support on the entire real space and have rational moment-generating functions. These distributions extend the class of bilateral phasetype distributions of [1] and the class of multivariate matrix-exponential distributions of [9]. We prove a characterization theorem stating that a random variable has a bilateral multivariate distribution if and only if all linear combinations of the coordinates have a univariate bilateral matrix-exponential distribution. As an application we demonstrate that certain multivariate disions, which are governed by the underlying Markov jump process generating a phasetype distribution, have a bilateral matrix-exponential distribution at the time of absorption, see also [4].

Original language	English
Journal	S I G M E T R I C S Performance Evaluation Review
Volume	39
Issue number	4
Pages (from-to)	25
ISSN	0163-5999
DOIs	https://doi.org/10.1145/2185395.2185405
Publication status	Published - 2012
Event	7th International Conference on Matrix-Analytic Methods in Stochastic Models (MAM7) - Columbia University, New York, NY, United States Duration: 13 Jun 2011 → 16 Jun 2011 http://portal.seas.columbia.edu/seas/MAM7/mam7.html

Conference

Conference	7th International Conference on Matrix-Analytic Methods in Stochastic Models (MAM7)
Location	Columbia University
Country/Territory	United States
City	New York, NY
Period	13/06/2011 → 16/06/2011
Internet address	http://portal.seas.columbia.edu/seas/MAM7/mam7.html

Bibliographical note

Abstract only.

Access to Document

10.1145/2185395.2185405

OpenUrl availability

Full text

Cite this

@article{61d19e8d13434adaba227e6a89836b12,

title = "Bilateral matrix-exponential distributions",

abstract = "In this article we define the classes of bilateral and multivariate bilateral matrix-exponential distributions. These distributions have support on the entire real space and have rational moment-generating functions. These distributions extend the class of bilateral phasetype distributions of [1] and the class of multivariate matrix-exponential distributions of [9]. We prove a characterization theorem stating that a random variable has a bilateral multivariate distribution if and only if all linear combinations of the coordinates have a univariate bilateral matrix-exponential distribution. As an application we demonstrate that certain multivariate disions, which are governed by the underlying Markov jump process generating a phasetype distribution, have a bilateral matrix-exponential distribution at the time of absorption, see also [4].",

author = "Mogens Bladt and Esparza, {Luz Judith R} and Nielsen, {Bo Friis}",

note = "Abstract only.; 7th International Conference on Matrix-Analytic Methods in Stochastic Models (MAM7) ; Conference date: 13-06-2011 Through 16-06-2011",

year = "2012",

doi = "10.1145/2185395.2185405",

language = "English",

volume = "39",

pages = "25",

journal = "S I G M E T R I C S Performance Evaluation Review",

issn = "0163-5999",

publisher = "ACM",

number = "4",

url = "http://portal.seas.columbia.edu/seas/MAM7/mam7.html",

}

TY - ABST

T1 - Bilateral matrix-exponential distributions

AU - Bladt, Mogens

AU - Esparza, Luz Judith R

AU - Nielsen, Bo Friis

N1 - Abstract only.

PY - 2012

Y1 - 2012

N2 - In this article we define the classes of bilateral and multivariate bilateral matrix-exponential distributions. These distributions have support on the entire real space and have rational moment-generating functions. These distributions extend the class of bilateral phasetype distributions of [1] and the class of multivariate matrix-exponential distributions of [9]. We prove a characterization theorem stating that a random variable has a bilateral multivariate distribution if and only if all linear combinations of the coordinates have a univariate bilateral matrix-exponential distribution. As an application we demonstrate that certain multivariate disions, which are governed by the underlying Markov jump process generating a phasetype distribution, have a bilateral matrix-exponential distribution at the time of absorption, see also [4].

AB - In this article we define the classes of bilateral and multivariate bilateral matrix-exponential distributions. These distributions have support on the entire real space and have rational moment-generating functions. These distributions extend the class of bilateral phasetype distributions of [1] and the class of multivariate matrix-exponential distributions of [9]. We prove a characterization theorem stating that a random variable has a bilateral multivariate distribution if and only if all linear combinations of the coordinates have a univariate bilateral matrix-exponential distribution. As an application we demonstrate that certain multivariate disions, which are governed by the underlying Markov jump process generating a phasetype distribution, have a bilateral matrix-exponential distribution at the time of absorption, see also [4].

U2 - 10.1145/2185395.2185405

DO - 10.1145/2185395.2185405

M3 - Conference abstract in journal

SN - 0163-5999

VL - 39

SP - 25

JO - S I G M E T R I C S Performance Evaluation Review

JF - S I G M E T R I C S Performance Evaluation Review

IS - 4

T2 - 7th International Conference on Matrix-Analytic Methods in Stochastic Models (MAM7)

Y2 - 13 June 2011 through 16 June 2011

ER -

Bilateral matrix-exponential distributions

Abstract

Conference

Bibliographical note

Access to Document

OpenUrl availability

Fingerprint

Cite this