{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T08:12:55Z","timestamp":1763367175703,"version":"3.41.0"},"reference-count":30,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation methods. An alternative approach to Monte Carlo simulation is the quasi-Monte Carlo method, which uses low-discrepancy sequences, instead of pseudorandom numbers, in simulation. Low-discrepancy sequences from different distributions can be obtained by the inverse transformation method, just like for pseudorandom numbers. In this paper, we present an acceptance-rejection algorithm for low-discrepancy sequences. We prove a convergence result, and present error bounds. We then use this acceptance-rejection algorithm to develop quasi-Monte Carlo versions of some well-known algorithms to generate beta and gamma distributions, and investigate the efficiency of these algorithms numerically. We also consider the simulation of the variance gamma model, a model used in computational finance, where the generation of these probability distributions are needed. Our results show that the acceptance-rejection technique can result in significant improvements in computing time over the inverse transformation method in the context of low-discrepancy sequences.<\/jats:p>","DOI":"10.1515\/mcma-2016-0104","type":"journal-article","created":{"date-parts":[[2016,6,2]],"date-time":"2016-06-02T10:01:28Z","timestamp":1464861688000},"page":"133-148","source":"Crossref","is-referenced-by-count":10,"title":["The acceptance-rejection method for low-discrepancy sequences"],"prefix":"10.1515","volume":"22","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":"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":[[2016,4,12]]},"reference":[{"key":"2023040101305239637_j_mcma-2016-0104_ref_000_w2aab2b8b2b1b7b1ab1b1b1Aa","doi-asserted-by":"crossref","unstructured":"A. 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