The Best Choice Problem for a Random Number of Objects

Previous article Next article The Best Choice Problem for a Random Number of ObjectsE. L. Presman and I. M. SoninE. L. Presman and I. M. Soninhttps://doi.org/10.1137/1117078PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 M. Gardner, Mathematical Games, Sci. Amer., 202 (1960), 150–156, 3 (1960), pp. 173–182 CrossrefGoogle Scholar2 E. B. Dynkin, Optimal choice of the stopping moment of a Markov process, Dokl. Akad. Nauk SSSR, 150 (1963), 238–240, (In Russian.) MR0154329 (27:4278) Google Scholar3 Evgenii B. Dynkin and , Aleksandr A. Yushkevich, Markov processes: Theorems and problems, Translated from the Russian by James S. Wood, Plenum Press, New York, 1969x+237 MR0242252 (39:3585a) CrossrefGoogle Scholar4 A. N. Shiryaev, Statistical Sequential Analysis, Izd-vo “Nauka”, Moscow, 1969, (In Russian.) Google Scholar5 S. M. Gusein-Zade, The problem of choice and the optimal stopping rule for a sequence of independent trials, Theory Prob. Applications, 11 (1966), 472–476 10.1137/1111050 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails The 1/e-strategy is sub-optimal for the problem of best choice under no informationStochastic Processes and their Applications, Vol. 150 Cross Ref Progressive stopping heuristics that excel in individual and competitive sequential search10 March 2022 | Theory and Decision, Vol. 36 Cross Ref Trapping the Ultimate Success5 January 2022 | Mathematics, Vol. 10, No. 1 Cross Ref The best choice problem with random arrivals: How to beat the 1/e -strategyStochastic Processes and their Applications, Vol. 19 Cross Ref Light weight model for intra mode selection in HEVC16 March 2021 | Multimedia Tools and Applications, Vol. 80, No. 14 Cross Ref HEVC Intra Mode Selection Using Benford’s Law25 June 2020 | Circuits, Systems, and Signal Processing, Vol. 40, No. 1 Cross Ref Secretary Problem with Possible Errors in Observation23 September 2020 | Mathematics, Vol. 8, No. 10 Cross Ref Guided filter based intra mode accelerator for HEVC16 April 2020 | Multimedia Tools and Applications, Vol. 79, No. 27-28 Cross Ref A unified approach for solving sequential selection problemsProbability Surveys, Vol. 17, No. none Cross Ref Intra mode selection using classical secretary problem (CSP) in high efficiency video coding (HEVC)22 July 2019 | Multimedia Tools and Applications, Vol. 78, No. 22 Cross Ref Generalized Sequential Stochastic Assignment ProblemStochastic Systems, Vol. 8, No. 4 Cross Ref Urn sampling distributions giving alternate correspondences between two optimal stopping problems19 September 2016 | Advances in Applied Probability, Vol. 48, No. 3 Cross Ref Dynamic Service Selection with Optimal Stopping and ‘Trivial Choice’29 May 2015 Cross Ref Secretary Problem29 September 2014 Cross Ref Optimal Stopping Rule for the No-Information Duration Problem with Random Horizon4 January 2016 | Advances in Applied Probability, Vol. 45, No. 4 Cross Ref Duration problem with multiple exchangesNumerical Algebra, Control and Optimization, Vol. 2, No. 2 Cross Ref Maximizing the probability of stopping on any of the last m successes in independent Bernoulli trials with random horizon1 July 2016 | Advances in Applied Probability, Vol. 43, No. 3 Cross Ref Sum the Multiplicative Odds to One and Stop14 July 2016 | Journal of Applied Probability, Vol. 47, No. 3 Cross Ref No-information secretary problems with cardinal payoffs and Poisson arrivalsStatistics & Probability Letters, Vol. 80, No. 3-4 Cross Ref A Random Arrival Time Best-Choice Problem with Uniform Prior on the Number of Arrivals5 May 2010 Cross Ref Extension on Cut-off Rules of Sequential Observation and Selection ProblemSystems Engineering - Theory & Practice, Vol. 28, No. 2 Cross Ref Sequential Observation and Selection with Rank-Dependent Payoffs: An Experimental StudyManagement Science, Vol. 52, No. 9 Cross Ref Secretary Problem15 August 2006 Cross Ref An Explicit Formula for the Optimal Gain in the Full-Information Problem of Owning a Relatively Best Object14 July 2016 | Journal of Applied Probability, Vol. 43, No. 1 Cross Ref An interactive method for the optimal selection problem with two decision makersEuropean Journal of Operational Research, Vol. 162, No. 3 Cross Ref What is Known About Robbins' Problem?14 July 2016 | Journal of Applied Probability, Vol. 42, No. 1 Cross Ref An application of prophet regions to optimal stopping with a random number of observationsOptimization, Vol. 53, No. 4 Cross Ref Why do these quite different best-choice problems have the same solutions?1 July 2016 | Advances in Applied Probability, Vol. 36, No. 2 Cross Ref Fuzzy stopping problems in continuous-time fuzzy stochastic systemsFuzzy Sets and Systems, Vol. 139, No. 2 Cross Ref Choosing either the best or the second best when the number of applicants is randomComputers & Mathematics with Applications, Vol. 46, No. 7 Cross Ref Optimal stopping on patterns in strings generated by independent random variables14 July 2016 | Journal of Applied Probability, Vol. 40, No. 1 Cross Ref The Dynamic and Stochastic Knapsack Problem with Random Sized ItemsOperations Research, Vol. 49, No. 1 Cross Ref Optimal stopping behavior with relative ranks: the secretary problem with unknown population size1 January 2000 | Journal of Behavioral Decision Making, Vol. 13, No. 4 Cross Ref Optimal Stopping Problems in a Stochastic and Fuzzy SystemJournal of Mathematical Analysis and Applications, Vol. 246, No. 1 Cross Ref The Dynamic and Stochastic Knapsack ProblemOperations Research, Vol. 46, No. 1 Cross Ref Quick solutions for general best choice problems in continuous timeCommunications in Statistics. 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