{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T05:34:15Z","timestamp":1740202455979,"version":"3.37.3"},"reference-count":10,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,7,6]],"date-time":"2024-07-06T00:00:00Z","timestamp":1720224000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,6]],"date-time":"2024-07-06T00:00:00Z","timestamp":1720224000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100009232","name":"University of Debrecen","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100009232","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2025,3]]},"abstract":"Abstract<\/jats:title>\n In this paper, sequences of trials having three outcomes are studied. The outcomes are labelled as success, failure of type I and failure of type II. A run is called at most \n \n $$1+1$$<\/jats:tex-math>\n \n \n 1<\/mml:mn>\n +<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> contaminated, if it contains at most one failure of type I and at most one failure of type II. The accompanying distribution for the length of the longest at most \n \n $$1+1$$<\/jats:tex-math>\n \n \n 1<\/mml:mn>\n +<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> contaminated run is obtained. The proof is based on a powerful lemma of Cs\u00e1ki, F\u00f6ldes and Koml\u00f3s. Besides a mathematical proof, simulation results supporting our theorem are also presented.<\/jats:p>","DOI":"10.1007\/s10998-024-00600-6","type":"journal-article","created":{"date-parts":[[2024,7,6]],"date-time":"2024-07-06T03:37:02Z","timestamp":1720237022000},"page":"78-93","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A limit theorem for runs containing two types of contaminations"],"prefix":"10.1007","volume":"90","author":[{"given":"Istv\u00e1n","family":"Fazekas","sequence":"first","affiliation":[]},{"given":"Borb\u00e1la","family":"Fazekas","sequence":"additional","affiliation":[]},{"given":"Michael Ochieng","family":"Suja","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,6]]},"reference":[{"key":"600_CR1","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/BF02795493","volume":"23","author":"P Erd\u0151s","year":"1970","unstructured":"P. Erd\u0151s, A. R\u00e9nyi, On a new law of large numbers. Anal. Math. 23, 103\u2013111 (1970)","journal-title":"Anal. Math."},{"key":"600_CR2","first-page":"219","volume-title":"Topics in Information Theory. Colloq. Math. Soc. J\u00e1nos Bolyai","author":"P Erd\u0151s","year":"1975","unstructured":"P. Erd\u0151s, P. R\u00e9v\u00e9sz, On the length of the longest head-run, in Topics in Information Theory. Colloq. Math. Soc. J\u00e1nos Bolyai, vol. 16, (North-Holland, Amsterdam, 1975), pp.219\u2013228"},{"issue":"4","key":"600_CR3","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/BF02020027","volume":"10","author":"A F\u00f6ldes","year":"1979","unstructured":"A. F\u00f6ldes, The limit distribution of the length of the longest head-run. Period. Math. Hung. 10(4), 301\u2013310 (1979)","journal-title":"Period. Math. 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Fazekas, B. Fazekas, M.O. Suja, Convergence rate for the longest T-contaminated runs of heads (paper with detailed proofs). (2023) arXiv:2302.06657"},{"key":"600_CR8","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.spl.2016.04.003","volume":"115","author":"S Eryilmaz","year":"2016","unstructured":"S. Eryilmaz, M. Gong, M. Xie, Generalized sooner waiting time problems in a sequence of trinary trials. Stat. Prob. Lett. 115, 70\u201378 (2016)","journal-title":"Stat. Prob. Lett."},{"issue":"3","key":"600_CR9","doi-asserted-by":"publisher","first-page":"593","DOI":"10.2307\/3215087","volume":"34","author":"M Koutras","year":"1997","unstructured":"M. Koutras, V. Alexandrou, Sooner waiting time problems in a sequence of trinary trials. J. Appl. Probab. 34(3), 593\u2013609 (1997)","journal-title":"J. Appl. Probab."},{"key":"600_CR10","doi-asserted-by":"crossref","unstructured":"I. Fazekas, B. Fazekas, M.O. Suja, Limit theorems for runs containing two types of contaminations (Paper with detailed proofs) (2023). arXiv:2309.11602","DOI":"10.1007\/s10998-024-00600-6"}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-024-00600-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-024-00600-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-024-00600-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T15:07:21Z","timestamp":1740150441000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-024-00600-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,6]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["600"],"URL":"https:\/\/doi.org\/10.1007\/s10998-024-00600-6","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"type":"print","value":"0031-5303"},{"type":"electronic","value":"1588-2829"}],"subject":[],"published":{"date-parts":[[2024,7,6]]},"assertion":[{"value":"6 January 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 July 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}