{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T10:14:16Z","timestamp":1775470456633,"version":"3.50.1"},"reference-count":19,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The ziggurat method is a fast random variable generation method introduced by Marsaglia and Tsang in a series of papers. We discuss how the ziggurat method can be implemented for low-discrepancy sequences, and present algorithms and numerical results when the method is used to generate samples from the normal and gamma distributions.<\/jats:p>","DOI":"10.1515\/mcma-2018-0008","type":"journal-article","created":{"date-parts":[[2018,3,28]],"date-time":"2018-03-28T22:17:19Z","timestamp":1522275439000},"page":"93-99","source":"Crossref","is-referenced-by-count":3,"title":["A quasi-Monte Carlo implementation of the ziggurat method"],"prefix":"10.1515","volume":"24","author":[{"given":"Nguyet","family":"Nguyen","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics , Youngstown State University , Youngstown , OH 44555-7994 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linlin","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Florida State University , Tallahassee , FL 32306-4510 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giray","family":"\u00d6kten","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Florida State University , Tallahassee , FL 32306-4510 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2018,3,28]]},"reference":[{"key":"2023040101343520737_j_mcma-2018-0008_ref_001_w2aab3b7b2b1b6b1ab1b3b1Aa","doi-asserted-by":"crossref","unstructured":"C.  Aistleitner and J.  Dick,\nLow-discrepancy point sets for non-uniform measures,\nActa Arith. 163 (2014), no. 4, 345\u2013369.\n10.4064\/aa163-4-4","DOI":"10.4064\/aa163-4-4"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_002_w2aab3b7b2b1b6b1ab1b3b2Aa","doi-asserted-by":"crossref","unstructured":"L.  Devroye,\nNon-Uniform Random Variate Generation,\nSpringer, New York, 1986.","DOI":"10.1007\/978-1-4613-8643-8"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_003_w2aab3b7b2b1b6b1ab1b3b3Aa","unstructured":"J. A.  Doornik,\nAn improved ziggurat method to generate normal random samples,\nTechnical Report, University of Oxford, 2005, http:\/\/www.doornik.com\/research\/ziggurat.pdf."},{"key":"2023040101343520737_j_mcma-2018-0008_ref_004_w2aab3b7b2b1b6b1ab1b3b4Aa","doi-asserted-by":"crossref","unstructured":"G.  Fishman,\nMonte Carlo,\nSpringer, New York, 1996.","DOI":"10.1007\/978-1-4757-2553-7"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_005_w2aab3b7b2b1b6b1ab1b3b5Aa","doi-asserted-by":"crossref","unstructured":"A.  G\u00f6nc\u00fc and G.  \u00d6kten,\nUniform point sets and the collision test,\nJ. Comput. Appl. Math. 259 (2014), 798\u2013804.\n10.1016\/j.cam.2013.07.019","DOI":"10.1016\/j.cam.2013.07.019"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_006_w2aab3b7b2b1b6b1ab1b3b6Aa","doi-asserted-by":"crossref","unstructured":"J.  Hartinger and J. R.  Kainhofer,\nNon-uniform low-discrepancy sequence generation and integration of singular integrands,\nMonte Carlo and Quasi-Monte Carlo Methods 2004,\nSpringer, Berlin (2006), 163\u2013179.","DOI":"10.1007\/3-540-31186-6_11"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_007_w2aab3b7b2b1b6b1ab1b3b7Aa","doi-asserted-by":"crossref","unstructured":"E.  Hlawka and R.  M\u00fcck,\nA transformation of equidistributed sequences,\nApplications of Number Theory to Numerical Analysis,\nAcademic Press, Cambridge (1972), 371\u2013388.","DOI":"10.1016\/B978-0-12-775950-0.50018-2"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_008_w2aab3b7b2b1b6b1ab1b3b8Aa","doi-asserted-by":"crossref","unstructured":"P. H.  Leong, G.  Zhang, D. U.  Lee, W.  Luk and J.  Villasenor,\nA Comment on the implementation of the Ziggurat method,\nJ. Stat. Softw. 12 (2005), no. 7, 1\u20134.","DOI":"10.18637\/jss.v012.i07"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_009_w2aab3b7b2b1b6b1ab1b3b9Aa","doi-asserted-by":"crossref","unstructured":"G.  Marsaglia and W. W.  Tsang,\nA fast, easily implemented method for sampling from decreasing or symmetric unimodal density functions,\nSIAM J. Sci. Stat. Comput. 5 (1984), no. 2, 349\u2013359.\n10.1137\/0905026","DOI":"10.1137\/0905026"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_010_w2aab3b7b2b1b6b1ab1b3c10Aa","doi-asserted-by":"crossref","unstructured":"G.  Marsaglia and W. W.  Tsang,\nA simple method for generating gamma variables,\nACM Trans. Math. Software 26 (2000), 363\u2013372.\n10.1145\/358407.358414","DOI":"10.1145\/358407.358414"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_011_w2aab3b7b2b1b6b1ab1b3c11Aa","doi-asserted-by":"crossref","unstructured":"G.  Marsaglia and W. W.  Tsang,\nThe ziggurat method for generating random variables,\nJ. Stat. Softw. 5 (2000), no. 8, 1\u20137.","DOI":"10.18637\/jss.v005.i08"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_012_w2aab3b7b2b1b6b1ab1b3c12Aa","doi-asserted-by":"crossref","unstructured":"M.  Matsumoto and T.  Nishimura,\nMersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,\nACM Trans. Model. Comput. Simul. 8 (1998), no. 1, 3\u201330.\n10.1145\/272991.272995","DOI":"10.1145\/272991.272995"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_013_w2aab3b7b2b1b6b1ab1b3c13Aa","doi-asserted-by":"crossref","unstructured":"H.  Niederreiter,\nError bounds for quasi-Monte Carlo integration with uniform point sets,\nJ. Comput. Appl. Math. 150 (2003), 283\u2013292.\n10.1016\/S0377-0427(02)00665-9","DOI":"10.1016\/S0377-0427(02)00665-9"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_014_w2aab3b7b2b1b6b1ab1b3c14Aa","doi-asserted-by":"crossref","unstructured":"N.  Nguyen and G.  \u00d6kten,\nThe acceptance-rejection method for low-discrepancy sequences,\nMonte Carlo Methods Appl. 22 (2016), no. 2, 133\u2013148.","DOI":"10.1515\/mcma-2016-0104"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_015_w2aab3b7b2b1b6b1ab1b3c15Aa","doi-asserted-by":"crossref","unstructured":"G.  \u00d6kten and W.  Eastman,\nRandomized quasi-Monte Carlo methods in pricing securities,\nJ. Econom. Dynam. Control 28 (2004), 2399\u20132426.\n10.1016\/j.jedc.2003.11.003","DOI":"10.1016\/j.jedc.2003.11.003"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_016_w2aab3b7b2b1b6b1ab1b3c16Aa","doi-asserted-by":"crossref","unstructured":"G.  \u00d6kten and A.  G\u00f6nc\u00fc,\nGenerating low-discrepancy sequences from the normal distribution: Box\u2013Muller or inverse transform?,\nMath. Comput. Model. 53 (2011), no. 5, 1268\u20131281.\n10.1016\/j.mcm.2010.12.011","DOI":"10.1016\/j.mcm.2010.12.011"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_017_w2aab3b7b2b1b6b1ab1b3c17Aa","doi-asserted-by":"crossref","unstructured":"I. M.  Sobol\u2019,\nUniformly distributed sequences with an additional uniform property,\nUSSR Comput. Math. Math. Phys. 16 (1976), no. 5, 236\u2013242.\n10.1016\/0041-5553(76)90154-3","DOI":"10.1016\/0041-5553(76)90154-3"},{"key":"2023040101343520737_j_mcma-2018-0008_ref_018_w2aab3b7b2b1b6b1ab1b3c18Aa","unstructured":"I. M.  Sobol\u2019,\nA primer for the Monte Carlo Method,\nCRC Press, Boca Raton, 1994."},{"key":"2023040101343520737_j_mcma-2018-0008_ref_019_w2aab3b7b2b1b6b1ab1b3c19Aa","doi-asserted-by":"crossref","unstructured":"H.  Zhu and J.  Dick,\nDiscrepancy bounds for deterministic acceptance-rejection samplers,\nElectron. J. Stat. 8 (2014), 678\u2013707.\n10.1214\/14-EJS898","DOI":"10.1214\/14-EJS898"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/mcma.2018.24.issue-2\/mcma-2018-0008\/mcma-2018-0008.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2018-0008\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2018-0008\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T20:48:46Z","timestamp":1680382126000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2018-0008\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,28]]},"references-count":19,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,15]]},"published-print":{"date-parts":[[2018,6,1]]}},"alternative-id":["10.1515\/mcma-2018-0008"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2018-0008","relation":{},"ISSN":["1569-3961","0929-9629"],"issn-type":[{"value":"1569-3961","type":"electronic"},{"value":"0929-9629","type":"print"}],"subject":[],"published":{"date-parts":[[2018,3,28]]}}}