Extremal processes, secretary problems and the 1/e law
- 1 December 1989
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 26 (4) , 722-733
- https://doi.org/10.2307/3214377
Abstract
We consider a class of secretary problems in which the order of arrival of candidates is no longer uniformly distributed. By a suitable embedding in a time-transformed extremal process it is shown that the asymptotic winning probability is again 1/e as in the classical situation. Extensions of the problem to more than one choice are also considered.Keywords
This publication has 16 references indexed in Scilit:
- On a joint strong approximation theorem for record and inter-record timesProbability Theory and Related Fields, 1987
- Embedding sequences of successive maxima in extremal processes, with applicationsJournal of Applied Probability, 1987
- Records in the presence of a linear trendAdvances in Applied Probability, 1987
- A Semigroup Approach to Poisson ApproximationThe Annals of Probability, 1986
- The Secretary Problem and Its Extensions: A ReviewInternational Statistical Review, 1983
- Some Elementary Results on Poisson Approximation in a Sequence of Bernoulli TrialsSIAM Review, 1978
- Weak Convergence to Extremal ProcessesThe Annals of Probability, 1975
- Inverses of extremal processesAdvances in Applied Probability, 1974
- The structure of extremal processesAdvances in Applied Probability, 1973
- Recognizing the Maximum of a SequenceJournal of the American Statistical Association, 1966