{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:42:08Z","timestamp":1777902128318,"version":"3.51.4"},"reference-count":29,"publisher":"SAGE Publications","issue":"11","license":[{"start":{"date-parts":[[2007,11,1]],"date-time":"2007-11-01T00:00:00Z","timestamp":1193875200000},"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":[[2007,11]]},"abstract":"<jats:p>\n                    The cross-entropy and minimum cross-entropy methods are well-known Monte Carlo simulation techniques for rare-event probability estimation and optimization. In this paper, we investigate how these methods can be eXtended to provide a general non-parametric cross-entropy framework based on \u03c6-divergence distance measures. We show how the \u03c7\n                    <jats:sup>2<\/jats:sup>\n                    distance, in particular, yields a viable alternative to the Kullback\u2014Leibler distance. The theory is illustrated with various eXamples from density estimation, rare-event simulation and continuous multi-eXtremal optimization.\n                  <\/jats:p>","DOI":"10.1177\/0037549707087067","type":"journal-article","created":{"date-parts":[[2008,2,12]],"date-time":"2008-02-12T09:34:02Z","timestamp":1202808842000},"page":"785-806","source":"Crossref","is-referenced-by-count":36,"title":["Generalized Cross-entropy Methods with Applications to Rare-event Simulation                 and Optimization"],"prefix":"10.1177","volume":"83","author":[{"given":"Z.I.","family":"Botev","sequence":"first","affiliation":[{"name":"Department of Mathematics The University of Queensland Brisbane 4072,                         Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.P.","family":"Kroese","sequence":"additional","affiliation":[{"name":"Department of Mathematics The University of Queensland Brisbane 4072, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"Taimre","sequence":"additional","affiliation":[{"name":"Department of Mathematics The University of Queensland Brisbane 4072, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2007,11,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4321-0"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s11009-005-6653-7"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/21.44019"},{"key":"atypb4","first-page":"30","volume":"3","author":"Havrda, J.H.","year":"1967","journal-title":"Kybernatica"},{"key":"atypb5","volume-title":"The generalized cross entropy method, with applications to probability density estimation","author":"Botev, Z.I.","year":"2006"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316849"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-4493-1"},{"key":"atypb8","volume-title":"Rare event probability estimation for static models via cross-entropy and importance sampling","author":"Homem-de-Mello, T."},{"key":"atypb9","volume-title":"Stochastic Methods for Optimization and Machine Learning","author":"Botev, Z.I.","year":"2005"},{"key":"atypb10","volume-title":"Generalized Maximum Entropy Principle (With applications). 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