English

The Best-or-Worst and the Postdoc problems with random number of candidates

Probability 2018-11-13 v2 Combinatorics

Abstract

In this paper we consider two variants of the Secretary problem: The Best-or-Worst and the Postdoc problems. We extend previous work by considering that the number of objects is not known and follows either a discrete Uniform distribution U[1,n]\mathcal{U}[1,n] or a Poisson distribution P(λ)\mathcal{P}(\lambda). We show that in any case the optimal strategy is a threshold strategy, we provide the optimal cutoff values and the asymptotic probabilities of success. We also put our results in relation with closely related work.

Keywords

Cite

@article{arxiv.1809.06390,
  title  = {The Best-or-Worst and the Postdoc problems with random number of candidates},
  author = {L. Bayon and P. Fortuny and J. M. Grau and M. M Ruiz and M. A. Oller-Marcen},
  journal= {arXiv preprint arXiv:1809.06390},
  year   = {2018}
}