{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:38:01Z","timestamp":1777901881719,"version":"3.51.4"},"reference-count":20,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[1998,4,1]],"date-time":"1998-04-01T00:00:00Z","timestamp":891388800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIMULATION"],"published-print":{"date-parts":[[1998,4]]},"abstract":"<jats:p>\n                    In this paper we present a technique for generating random variates from an empirical distribution using the matrix exponential representation of the distribution. In our experience, a matrix exponential representation of an empirical distribution produces random variates with an excellent fit with the empirical distribution. This technique is particularly important when the empirical data is very bursty, i.e., has a high variance. In this paper we discuss how to find the matrix exponential representation of an empirical distribution and we present our technique for generating random variates from the empirical distribution using its matrix exponential representation. We show how the matrix exponential representation of an empirical distribution is found through an example and then we show that matrix exponential random variates are an excellent fit with the empirical data through an \u03c7\n                    <jats:sup>2<\/jats:sup>\n                    goodness-of-fit test.\n                  <\/jats:p>","DOI":"10.1177\/003754979807000402","type":"journal-article","created":{"date-parts":[[2007,3,18]],"date-time":"2007-03-18T03:46:49Z","timestamp":1174189609000},"page":"224-230","source":"Crossref","is-referenced-by-count":3,"title":["Generating Matrix Exponential Random Variates"],"prefix":"10.1177","volume":"70","author":[{"given":"E.","family":"Brown","sequence":"first","affiliation":[{"name":"Computer Science Telecommunication Program University of Missouri-Kansas City 5100 Rockhill Road, Kansas City, MO 64110"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Place","sequence":"additional","affiliation":[{"name":"Computer Science Telecommunication Program University of Missouri-Kansas City 5100 Rockhill Road, Kansas City, MO 64110"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Van de Liefvoort","sequence":"additional","affiliation":[{"name":"Computer Science Telecommunication Program University of Missouri-Kansas City 5100 Rockhill Road, Kansas City, MO 64110"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[1998,4,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1145\/130069.130114"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-7386-9"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-48850-4_4"},{"key":"atypb4","unstructured":"Efron, B., and LePage, R. 1992. \"Introduction to Bootstrap.\" Exploring the Limits of Bootstrap , R. LePage and L. Billiard, editors, Wiley, New York, 1992, pp 3-10."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-4541-9"},{"key":"atypb6","volume-title":"The Theory of Matrices","author":"Gantmacher, F.","year":"1959"},{"key":"atypb7","volume-title":"Matrix Computations","author":"Golub, G.","year":"1996"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(83)90059-9"},{"key":"atypb9","volume-title":"Modern Statistical Systems and GPSS Simulation","author":"Karian, Z.","year":"1991"},{"key":"atypb10","volume-title":"Simulation Modeling and Analysis","author":"Law, A.","year":"1991"},{"key":"atypb11","volume-title":"The Moment Problem for Continuous Distributions.\" Technical Report CM-1990-02","author":"Van de Liefvoort, A.","year":"1990"},{"key":"atypb12","volume-title":"Queuing Theory: A Linear Algebraic Approach","author":"Lipsky, L.","year":"1992"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/1020098"},{"key":"atypb14","volume-title":"Matrix-Geometric Solutions in Stochastic Models","author":"Neuts, M.F.","year":"1981"},{"key":"atypb15","volume-title":"Phase-Type Distributions: A Bibliography.\" Report 89-105","year":"1989"},{"key":"atypb16","volume-title":"Computer System Performance Modeling","author":"Saur, C.H.","year":"1981"},{"key":"atypb17","volume-title":"The Problem of Moments","author":"Shohat, J.A.","year":"1963"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"Stieltjes, T. 1894. Recherches sur les Fractions Continues, Ann. Fac. Sci. Univ., Toulouse 8, pp 1-122, 1894.","DOI":"10.5802\/afst.108"},{"key":"atypb19","first-page":"1","volume":"9","year":"1894","journal-title":"Ann. Fac. Sci. Univ."},{"key":"atypb20","volume-title":"A Survey of Numerical Mathematics","author":"Young, D.","year":"1973"}],"container-title":["SIMULATION"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/003754979807000402","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/003754979807000402","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T11:12:02Z","timestamp":1777633922000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/003754979807000402"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,4]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,4]]}},"alternative-id":["10.1177\/003754979807000402"],"URL":"https:\/\/doi.org\/10.1177\/003754979807000402","relation":{},"ISSN":["0037-5497","1741-3133"],"issn-type":[{"value":"0037-5497","type":"print"},{"value":"1741-3133","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,4]]}}}