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About 2,081 papers for “Partially ordered set”

Majorization on a partially ordered set

F. K. Hwang · Proceedings of the American Mathematical Society · 1979

We extend the classical concept of set majorization to the case where the set is partially ordered. We give a useful property which characterizes majorization on a partially ordered set. Quite unexpectedly, the proof of this property relies on a theorem of Shapley on convex games. We also give a theorem which is parallel to the Schur-Ostrowski theorem in comparing two sets of parameters in a function.

Cited by 16

Majorization on a Partially Ordered Set

F. K. Hwang · Proceedings of the American Mathematical Society · 1979

We extend the classical concept of set majorization to the case where the set is partially ordered.We give a useful property which characterizes majorization on a partially ordered set.Quite unexpectedly, the proof of this property relies on a theorem of Shapley on convex games.We also give a theorem which is parallel to the Schur-Ostrowski theorem in comparing two sets of parameters in a function.

Cited by 1Open access

On subsets of a partially ordered set

S. D. McCartan · Mathematical Proceedings of the Cambridge Philosophical Society · 1966

In this paper we discuss the structure of a partially ordered set X by studying in detail certain subsets of X .

Cited by 5

On Supermartingales with Partially Ordered Parameter Set

Gerardo Sánchez Licea · Theory of Probability and Its Applications · 1969

Previous article Next article On Supermartingales with Partially Ordered Parameter SetG. LiceaG. Liceahttps://doi.org/10.1137/1114014PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Lester L. Helms, Mean convergence of martingales, Trans. Amer. Math. Soc., 87 (1958), 439–446 MR0094841 0080.11904 CrossrefGoogle Scholar[2] P. A. Meyer, Probability and Potential, Blaisdell Publ. Comp., Waltham, Massachusetts, Toronto, London, Google Scholar[3] Aurel Cornea and , Gabriela Licea, General optional sampling of supermartingales, Rev. Roumaine Math. Pures Appl., 10 (1965), 1349–1367 MR0199910 0137.11502 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Set-Indexed Stochastic Processes and PredictabilityTheory of Probability & Its Applications, Vol. 37, No. 1 | 28 July 2006AbstractPDF (819 KB) Volume 14, Issue 1| 1969Theory of Probability & Its Applications1-181 History Submitted:02 December 1967Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1114014Article page range:pp. 135-137ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Cited by 2

Order-compatible topologies on a partially ordered set

E. S. Wolk · Proceedings of the American Mathematical Society · 1958

Introduction.Let X be a partially ordered set (poset) with respect to a relation g, and possessing least and greatest elements 0 and / respectively.There are many known ways of using the order properties of X to define an "intrinsic" topology on X.It is our purpose in this note, instead of considering certain special topologies of this type, to introduce a class of topologies on X which are compatible, in a natural sense, with its order.To this end, let us call a subset S of X up-directed (down-directed) il and only if for all xES and yES there exists zES with z^x,zg^y(z^x, z^y).Also, following

Cited by 20

Uniform k-Tuple Partially Rank-Ordered Set Sampling

Marvin Javier, Kaushik Ghosh · Communication in Statistics- Theory and Methods · 2021

Ranked Set Sampling (RSS), introduced by McIntyre, and other related methods, such as Partially Rank-Ordered Set Sampling (PROSS), have shown that inclusion of a ranking mechanism produces estimators with lower variance than their simple random sample (SRS)-based counterparts. Like RSS, PROSS takes only one measurement from each partially ranked-ordered set. We propose a sampling plan called Uniform k-Tuple Partially Rank-Ordered (UKPRSS) where a measurement is collected from each group of a partially rank-ordered set. This article demonstrates estimators from UKPRSS have lower variance than their SRS counterparts. In addition, there is a reduction in the number units needing to be screened when compared to PROSS. Estimation of the mean and distribution function are investigated theoretically.

Cited by 0

Information content of partially rank-ordered set samples

Armin Hatefi, Mohammad Jafari Jozani · arXiv (Cornell University) · 2015

Partially rank-ordered set (PROS) sampling is a generalization of ranked set sampling in which rankers are not required to fully rank the sampling units in each set, hence having more flexibility to perform the necessary judgemental ranking process. The PROS sampling has a wide range of applications in different fields ranging from environmental and ecological studies to medical research and it has been shown to be superior over ranked set sampling and simple random sampling for estimating the population mean. In this paper, we study the Fisher information content and uncertainty structure of the PROS samples and compare them with those of simple random sample (SRS) and ranked set sample (RSS) counterparts of the same size from the underlying population. We study the uncertainty structure in terms of the Shannon entropy, Renyi entropy and Kullback-Leibler (KL) discrimination measures. Several examples including the FI of PROS samples from the location-scale family of distributions as well as a regression model are discussed.

Cited by 3Open access