{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:41:22Z","timestamp":1682502082941},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p>Let <jats:italic>T<\/jats:italic> be a stopping time associated with a sequence of independent and identically distributed or exchangeable random variables taking values in {0, 1, 2, \u2026, <jats:italic>m<\/jats:italic>}, and let <jats:italic>S<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>T<\/jats:italic>,<jats:italic>i<\/jats:italic>\n               <\/jats:sub> be the stopped sum denoting the number of appearances of outcome '<jats:italic>i<\/jats:italic>' in <jats:italic>X<\/jats:italic>\n               <jats:sub>1<\/jats:sub>, \u2026, <jats:italic>X<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>T<\/jats:italic>\n               <\/jats:sub>, 0 \u2264 <jats:italic>i<\/jats:italic> \u2264 <jats:italic>m<\/jats:italic>. In this paper we present results revealing that, if the distribution of <jats:italic>T<\/jats:italic> is known, then we can also derive the joint distribution of (<jats:italic>T<\/jats:italic>, <jats:italic>S<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>T<\/jats:italic>,0<\/jats:sub>, <jats:italic>S<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>T<\/jats:italic>,1<\/jats:sub>, \u2026, <jats:italic>S<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>T<\/jats:italic>,<jats:italic>m<\/jats:italic>\n               <\/jats:sub>). Two applications, which have independent interest, are offered to illustrate the applicability and the usefulness of the main results.<\/jats:p>","DOI":"10.1017\/s0021900200011372","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:51:11Z","timestamp":1459263071000},"page":"483-491","source":"Crossref","is-referenced-by-count":0,"title":["On the Joint Distribution of Stopping Times and Stopped Sums in Multistate Exchangeable Trials"],"prefix":"10.1017","volume":"51","author":[{"given":"M. V.","family":"Boutsikas","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D. L.","family":"Antzoulakos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. C.","family":"Rakitzis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"key":"S0021900200011372_ref16","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348766"},{"key":"S0021900200011372_ref4","volume-title":"Runs and Scans with Applications","year":"2002"},{"key":"S0021900200011372_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s11009-009-9147-1"},{"key":"S0021900200011372_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2006.05.009"},{"key":"S0021900200011372_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4749-0_10"},{"key":"S0021900200011372_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00773603"},{"key":"S0021900200011372_ref13","volume-title":"A First Course in Stochastic Processes","year":"1975"},{"key":"S0021900200011372_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2011.02.002"},{"key":"S0021900200011372_ref11","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1175267164"},{"key":"S0021900200011372_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02530529"},{"key":"S0021900200011372_ref9","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1294170521"},{"key":"S0021900200011372_ref8","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1231340230"},{"key":"S0021900200011372_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2008.01.002"},{"key":"S0021900200011372_ref6","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1013540248"},{"key":"S0021900200011372_ref17","doi-asserted-by":"publisher","DOI":"10.1023\/A:1003756712643"},{"key":"S0021900200011372_ref3","doi-asserted-by":"publisher","DOI":"10.1023\/A:1003170829230"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200011372","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:08:13Z","timestamp":1682500093000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200011372\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6]]},"references-count":16,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["S0021900200011372"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200011372","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6]]}}}