Odds theorem with multiple selection chances

Katsunori Ano, Hideo Kakinuma, Naoto Miyoshi

研究成果: Article査読

8 被引用数 (Scopus)

抄録

We study the multi-selection version of the so-called odds theorem by Bruss (2000). We observe a finite number of independent 0/1 (failure/success) random variables sequentially and want to select the last success. We derive the optimal selection rule when m (≥ 1) selection chances are given and find that the optimal rule has the form of a combination of multiple odds-sums. We provide a formula for computing the maximum probability of selecting the last success when we havemselection chances and also provide closed-form formulae for m = 2 and 3. For m = 2, we further give the bounds for the maximum probability of selecting the last success and derive its limit as the number of observations goes to ∞. An interesting implication of our result is that the limit of the maximum probability of selecting the last success for m = 2 is consistent with the corresponding limit for the classical secretary problem with two selection chances.

本文言語English
ページ(範囲)1093-1104
ページ数12
ジャーナルJournal of Applied Probability
47
4
DOI
出版ステータスPublished - 2010 12

ASJC Scopus subject areas

  • 統計学および確率
  • 数学 (全般)
  • 統計学、確率および不確実性

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