NDLI: An overview of multivariate gamma distributions as seen from a (multivariate) matrix exponential perspective

Content Provider	ACM Digital Library
Author	Bladt, Mogens Nielsen, Bo Friis
Abstract	Numerous definitions of multivariate exponential and gamma distributions can be retrieved from the literature [4]. These distribtuions belong to the class of Multivariate Matrix-- Exponetial Distributions (MVME) whenever their joint Laplace transform is a rational function. The majority of these distributions further belongs to an important subclass of MVME distributions [5, 1] where the multivariate random vector can be interpreted as a number of simultaneously collected rewards during sojourns in a the states of a Markov chain with one absorbing state, the rest of the states being transient. We present the corresponding representations for all such distributions. In this way we obtain a unification of the variety of existing distributions as well as a deeper understanding of their probabilistic nature and a clarification of their similarities and differences. In particular one may easily generalize or combine any of the known distributions by modifying the generators adequately. Also, it is straightforward to simulate from this class. Thus, by identifying distributions as belonging to this subclass it becomes apparent how to simulate from most previously discussed distributions with rational Laplace transform. In a longer perspective stochastic and statistical analysis for MVME will in particular apply to any of the previously defined distributions. Multivariate gamma distributions have been used in a variety of fields like hydrology, [11], [10], [6], space (wind modeling) [9] reliability [3], [7], traffic modeling [8], and, finance [2]. It is our hope that our the paper will assist practitioners in formulating and analyzing models in a much more transparent and easily accessible way.
Starting Page	34
Ending Page	34
Page Count	1
File Format	PDF
ISSN	01635999
DOI	10.1145/2185395.2185425
Journal	ACM SIGMETRICS Performance Evaluation Review (PERV)
Volume Number	39
Issue Number	4
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-01-10
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Computer Networks and Communications Hardware and Architecture Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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