An improved procedure for selecting the better of two bernoulli populations

Donald A. Berry; Milton Sobel

doi:10.1080/01621459.1973.10481459

An improved procedure for selecting the better of two bernoulli populations

Donald A. Berry, Milton Sobel

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

A truncated play-the-winner sampling procedure for selecting the better of Bernoulli populations π₁ and π₂ is considered. Associated with π_i is success probability p_i where p₁ ≥ p₂. The procedure is designed to select π₁ with probability at least P* whenever p₁ − p₂ ≥ Δ *; P* and Δ* are preassigned constants. This truncation procedure is shown to be uniformly asymptotically better than the scheme of Sobel and Weiss [6] with regard to both minimizing the expected total number of trials and minimizing the expected number of trials on π₂. Numerical results show that the improvement can be substantial for small values of p₁ and p₂.

Original language	English (US)
Pages (from-to)	979-984
Number of pages	6
Journal	Journal of the American Statistical Association
Volume	68
Issue number	344
DOIs	https://doi.org/10.1080/01621459.1973.10481459
State	Published - Dec 1973
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1080/01621459.1973.10481459

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title = "An improved procedure for selecting the better of two bernoulli populations",

abstract = "A truncated play-the-winner sampling procedure for selecting the better of Bernoulli populations π1 and π2 is considered. Associated with πi is success probability pi where p1 ≥ p2. The procedure is designed to select π1 with probability at least P* whenever p1 − p2 ≥ Δ *; P* and Δ* are preassigned constants. This truncation procedure is shown to be uniformly asymptotically better than the scheme of Sobel and Weiss [6] with regard to both minimizing the expected total number of trials and minimizing the expected number of trials on π2. Numerical results show that the improvement can be substantial for small values of p1 and p2.",

author = "Berry, {Donald A.} and Milton Sobel",

note = "Funding Information: * Donald A. Berry is assistant professor and Milton Sobel is professor, both with the School of Statistics, University of Minnesota, Minneapolis, Minn. 55455. This research was supported by National Science Foundation Grant No. 28922X.",

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AU - Sobel, Milton

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N2 - A truncated play-the-winner sampling procedure for selecting the better of Bernoulli populations π1 and π2 is considered. Associated with πi is success probability pi where p1 ≥ p2. The procedure is designed to select π1 with probability at least P* whenever p1 − p2 ≥ Δ *; P* and Δ* are preassigned constants. This truncation procedure is shown to be uniformly asymptotically better than the scheme of Sobel and Weiss [6] with regard to both minimizing the expected total number of trials and minimizing the expected number of trials on π2. Numerical results show that the improvement can be substantial for small values of p1 and p2.

AB - A truncated play-the-winner sampling procedure for selecting the better of Bernoulli populations π1 and π2 is considered. Associated with πi is success probability pi where p1 ≥ p2. The procedure is designed to select π1 with probability at least P* whenever p1 − p2 ≥ Δ *; P* and Δ* are preassigned constants. This truncation procedure is shown to be uniformly asymptotically better than the scheme of Sobel and Weiss [6] with regard to both minimizing the expected total number of trials and minimizing the expected number of trials on π2. Numerical results show that the improvement can be substantial for small values of p1 and p2.

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An improved procedure for selecting the better of two bernoulli populations

Abstract

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