{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:34:16Z","timestamp":1759970056377,"version":"build-2065373602"},"reference-count":9,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T00:00:00Z","timestamp":1735862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we study the usual coin tossing experiment. We call a run at most T-contaminated, if it contains at most T tails. We approximate the distribution of the length of the longest at most T-contaminated runs. We offer a more precise approximation than the previous one.<\/jats:p>","DOI":"10.3390\/e27010033","type":"journal-article","created":{"date-parts":[[2025,1,3]],"date-time":"2025-01-03T05:02:02Z","timestamp":1735880522000},"page":"33","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Convergence Rate for the Longest at Most T-Contaminated Runs of Heads"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9934-2972","authenticated-orcid":false,"given":"Istv\u00e1n","family":"Fazekas","sequence":"first","affiliation":[{"name":"Faculty of Informatics, University of Debrecen, Kassai Street 26, 4028 Debrecen, Hungary"}]},{"given":"Borb\u00e1la","family":"Fazekas","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, University of Debrecen, Egyetem Square 1, 4032 Debrecen, Hungary"}]},{"given":"L\u00e1szl\u00f3","family":"F\u00f3ri\u00e1n","sequence":"additional","affiliation":[{"name":"Faculty of Informatics, University of Debrecen, Kassai Street 26, 4028 Debrecen, Hungary"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/BF02795493","article-title":"On a new law of large numbers","volume":"23","author":"Erdos","year":"1970","journal-title":"J. Analyse Math."},{"key":"ref_2","first-page":"219","article-title":"On the length of the longest head-run","volume":"Volume 16","author":"Erdos","year":"1977","journal-title":"Topics in Information Theory (Second Colloq., Keszthely, 1975)"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/BF02020027","article-title":"The limit distribution of the length of the longest head-run","volume":"10","year":"1979","journal-title":"Period. Math. Hungar."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.4153\/CJM-1993-070-x","article-title":"The a.s. limit distribution of the longest head run","volume":"45","year":"1993","journal-title":"Canad. J. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF00699107","article-title":"An extreme value theory for long head runs","volume":"72","author":"Gordon","year":"1986","journal-title":"Probab. Theory Relat. Fields"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.spl.2017.06.020","article-title":"On the length of the longest head run","volume":"130","author":"Novak","year":"2017","journal-title":"Statist. Probab. Lett."},{"key":"ref_7","first-page":"539","article-title":"The Erdos-R\u00e9nyi Law in Distribution, for Coin Tossing and Sequence Matching","volume":"18","author":"Arratia","year":"2008","journal-title":"Ann. Statist."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"110059","DOI":"10.1016\/j.spl.2024.110059","article-title":"Convergence rate for the longest T-contaminated runs of heads","volume":"208","author":"Fazekas","year":"2024","journal-title":"Statist. Probab. Lett."},{"key":"ref_9","first-page":"321","article-title":"Limit theorems for Erdos-R\u00e9nyi type problems","volume":"22","year":"1987","journal-title":"Studia Sci. Math. Hungar."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/1\/33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:22:24Z","timestamp":1759918944000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/1\/33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,3]]},"references-count":9,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["e27010033"],"URL":"https:\/\/doi.org\/10.3390\/e27010033","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2025,1,3]]}}}