Open Access
December, 1984 On Karlin's Conjecture for Random Replacement Sampling Plans
O. Krafft, M. Schaefer
Ann. Statist. 12(4): 1528-1535 (December, 1984). DOI: 10.1214/aos/1176346809


In 1974 Karlin introduced the concept of random replacement schemes and conjectured that the componentwise monotonicity of the replacement probabilities (condition A) is equivalent to a corresponding ordering of expectations of all functions $\phi$ from a certain class $\mathscr{C}_K$ (condition B). In this paper it is shown that A implies B for sample sizes $n \leq 5$ and--provided the sample space is sufficiently large--also for $n \geq 6$. By a counterexample it is shown that $\mathscr{C}_K$ is not suitable for A being implied by B, i.e. one direction of Karlin's conjecture is disproved.


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O. Krafft. M. Schaefer. "On Karlin's Conjecture for Random Replacement Sampling Plans." Ann. Statist. 12 (4) 1528 - 1535, December, 1984.


Published: December, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0598.62010
MathSciNet: MR760705
Digital Object Identifier: 10.1214/aos/1176346809

Primary: 62D05
Secondary: 05A20 , 60G05

Keywords: combinatorial inequalities , partial ordering , Random replacement sampling plans

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 4 • December, 1984
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