On Karlin's conjecture for random replacement sampling plans
type: Item
instance of: scholarly article
title: On Karlin's conjecture for random replacement sampling plans
zbMATH Open document ID: 0598.62010
author: O. Krafft
author: M. Schaefer
published in: The Annals of Statistics
publication date: 1984-01-01T00:00:00Z
review text: In ibid. 2, 1065-1094 (1974; Zbl 0306.62004) \textit{S. 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 \({\mathcal C}_ K\) (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 \({\mathcal C}_ K\) is not suitable for A being implied by B, i.e. one direction of Karlin's conjecture is disproved.
Mathematics Subject Classification ID: 62D05
Mathematics Subject Classification ID: 60G05
Mathematics Subject Classification ID: 05A20
zbMATH DE Number: 3965166
zbMATH Keywords: combinatorial inequalities, partial ordering
zbMATH Keywords: random replacement schemes
zbMATH Keywords: componentwise monotonicity
zbMATH Keywords: ordering of expectations
zbMATH Keywords: Karlin's conjecture
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346809
OpenAlex ID: W2046765530
Wikidata QID: Q123219644
DOI: 10.1214/AOS/1176346809
description: scientific article; zbMATH DE number 3965166