Sankhya: The Indian Journal of Statistics

1995, Volume 57, Series B, Pt. 1, pp. 76--84

A POOLING METHODOLOGY FOR COEFFICIENT OF VARIATION

By

A. A. K. MAJUMDAR, Jahangirnagar University

SUMMARY.  This paper extends the classical secretary problem with three stops to the case when offers arrive in [0, T], where T itself is a random variable, uniformly distributed on [0,1]. A traveler, observing relative ranks, wishes to select the absolute best in three stops before the random time T; if he succeeds, it would be termed his "win". The objective is to devise a stopping rule which stops at and accepts three applicants before T such that the probability of win is maximized. The dynamic programming has been employed to show that the optimal policy is characterized by three critical constants $\alpha_3$, $\alpha_2$ and $\alpha_1$ such that the traveler makes his first, second and third stops at the earliest candidates after $\alpha_3$, $\alpha_2$ and $\alpha_1$ respectively.

AMS (1991) subject classification.  90C39.

Key words and phrases. Classical secretary problem, best-choice problem, random termination, dynamic programming.

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This article in mathematical reviews.