{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T03:44:55Z","timestamp":1648871095796},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T00:00:00Z","timestamp":1221177600000},"content-version":"unspecified","delay-in-days":4669,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[1995,12]]},"abstract":"<jats:p>We derive identities for the probability that at least <jats:italic>a<\/jats:italic><jats:sub>1<\/jats:sub> and at least <jats:italic>a<\/jats:italic><jats:sub>2<\/jats:sub>, and for the probability that exactly <jats:italic>a<\/jats:italic><jats:sub>1<\/jats:sub> and exactly <jats:italic>a<\/jats:italic><jats:sub>2<\/jats:sub>, out of <jats:italic>n<\/jats:italic> and <jats:italic>N<\/jats:italic> events occur (1 \u2264 <jats:italic>a<\/jats:italic><jats:sub>1<\/jats:sub> \u2264 <jats:italic>n<\/jats:italic>, 1 \u2264 <jats:italic>a<\/jats:italic><jats:sub>2<\/jats:sub> \u2264 <jats:italic>N<\/jats:italic>). From this, we produce multivariate permutation hybrid upper bounds, and a multivariate Bonferroni-type upper bound which includes Galambos and Xu's [2] optimal result. The methodology generalizes that of Hoppe and Seneta [3, \u00a75]. A numerical example is given.<\/jats:p>","DOI":"10.1017\/s096354830000170x","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T07:13:24Z","timestamp":1221203604000},"page":"331-342","source":"Crossref","is-referenced-by-count":1,"title":["Multivariate Identities, Permutation and Bonferroni Upper Bounds"],"prefix":"10.1017","volume":"4","author":[{"given":"Tuhao","family":"Chen","sequence":"first","affiliation":[]},{"given":"E.","family":"Seneta","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"S096354830000170X_ref004","doi-asserted-by":"publisher","DOI":"10.2307\/1403754"},{"key":"S096354830000170X_ref005","doi-asserted-by":"publisher","DOI":"10.1017\/S0021900200104164"},{"key":"S096354830000170X_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01830980"},{"key":"S096354830000170X_ref010","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-842X.1988.tb00462.x"},{"key":"S096354830000170X_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1993-1146860-7"},{"key":"S096354830000170X_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/1403808"},{"key":"S096354830000170X_ref007","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.4710280807"},{"key":"S096354830000170X_ref008","first-page":"509","article-title":"Improved Bonferroni inequalities","volume":"33","author":"Margaritescu","year":"1988","journal-title":"Rev. Roum. Math. Pures Appl."},{"key":"S096354830000170X_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-2817-9_9"},{"key":"S096354830000170X_ref009","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177697743"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096354830000170X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T16:06:51Z","timestamp":1557763611000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096354830000170X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,12]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1995,12]]}},"alternative-id":["S096354830000170X"],"URL":"https:\/\/doi.org\/10.1017\/s096354830000170x","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,12]]}}}