{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:16:50Z","timestamp":1760188610779,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T00:00:00Z","timestamp":1559001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The widely known generators of Poisson random variables are associated with different modifications of the algorithm based on the convergence in probability of a sequence of uniform random variables to the created stochastic number. However, in some situations, this approach yields different discrete Poisson probability distributions and skipping in the generated numbers. This article offers a new approach for creating Poisson random variables based on the complete twister generator of uniform random variables, using cumulative frequency technology. The simulation results confirm that probabilistic and frequency distributions of the obtained stochastic numbers completely coincide with the theoretical Poisson distribution. Moreover, combining this new approach with the tuning algorithm of basic twister generation allows for a significant increase in length of the created sequences without using additional RAM of the computer.<\/jats:p>","DOI":"10.3390\/a12060114","type":"journal-article","created":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T11:18:09Z","timestamp":1559042289000},"page":"114","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Poisson Twister Generator by Cumulative Frequency Technology"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7735-4016","authenticated-orcid":false,"given":"Aleksei F.","family":"Deon","sequence":"first","affiliation":[{"name":"Department of Information Systems and Computer Science, Bauman Moscow State Technical University, 2nd Baumanskaya St., 5\/1, 105005 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5861-3641","authenticated-orcid":false,"given":"Yulian A.","family":"Menyaev","sequence":"additional","affiliation":[{"name":"Winthrop P. Rockefeller Cancer Institute, University of Arkansas for Medical Sciences, 4301 W. Markham St., Little Rock, AR 72205, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,28]]},"reference":[{"key":"ref_1","unstructured":"Feller, W. (2008). An Introduction to Probability Theory and Its Applications, John Wiley & Sons. [3rd ed.]."},{"key":"ref_2","unstructured":"Gnedenko, B. (1998). Theory of Probability, CRC Press. [6th ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6789","DOI":"10.1080\/03610926.2014.901375","article-title":"Characterizations of discrete compound poisson distribution","volume":"45","author":"Zhang","year":"2016","journal-title":"Commun. Stat.-Theory Method."},{"key":"ref_4","first-page":"21","article-title":"Power low distribution: method of multi-scale inferential statistics","volume":"1","author":"Guerriero","year":"2012","journal-title":"J. Mod. Math. 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