{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T07:41:12Z","timestamp":1682494872023},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p>Suppose that both you and your friend toss an unfair coin<jats:italic>n<\/jats:italic>times, for which the probability of heads is equal to \u03b1. What is the probability that you obtain at least<jats:italic>d<\/jats:italic>more heads than your friend if you make<jats:italic>r<\/jats:italic>additional tosses? We obtain asymptotic and monotonicity\/convexity properties for this competing probability as a function of<jats:italic>n<\/jats:italic>, and demonstrate surprising phase transition phenomenon as the parameters<jats:italic>d<\/jats:italic>,<jats:italic>r<\/jats:italic>, and \u03b1 vary. Our main tools are integral representations based on Fourier analysis.<\/jats:p>","DOI":"10.1017\/s0021900200009505","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:49:44Z","timestamp":1459262984000},"page":"731-744","source":"Crossref","is-referenced-by-count":0,"title":["Probabilities of Competing Binomial Random Variables"],"prefix":"10.1017","volume":"49","author":[{"given":"Wenbo V.","family":"Li","sequence":"first","affiliation":[]},{"given":"Vladislav V.","family":"Vysotsky","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"key":"S0021900200009505_ref1","doi-asserted-by":"crossref","first-page":"29","DOI":"10.26493\/1855-3974.178.12b","volume":"4","year":"2011","journal-title":"Ars Math. Contemp."},{"key":"S0021900200009505_ref8","volume-title":"CRC Standard Mathematical Tables and Formulae","year":"2002"},{"key":"S0021900200009505_ref7","volume-title":"A First Course in Probability","year":"2010"},{"key":"S0021900200009505_ref3","volume-title":"Fundamentals of Probability","year":"2005"},{"key":"S0021900200009505_ref5","volume-title":"A First Course in Stochastic Processes","year":"1968"},{"key":"S0021900200009505_ref4","volume-title":"An Introduction to Probability Theory and Its Applications","volume":"II.","year":"1966"},{"key":"S0021900200009505_ref6","doi-asserted-by":"publisher","DOI":"10.1080\/00949655.2010.484901"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200009505","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T07:12:15Z","timestamp":1682493135000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200009505\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9]]},"references-count":7,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2012,9]]}},"alternative-id":["S0021900200009505"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200009505","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,9]]}}}