Some order relations between selection and inclusion probabilities for PPSWOR sampling scheme
type: Item
instance of: scholarly article
title: Some order relations between selection and inclusion probabilities for PPSWOR sampling scheme
zbMATH Open document ID: 0755.62020
DOI: 10.1007/BF02613629
author: T. J. Rao
author: Bikas K. Sinha
author: S. Sengupta
published in: Metrika
publication date: 1992-06-28T00:00:00Z
full work available at URL: https://eudml.org/doc/176369
review text: A sample of size \(n\) is selected from a finite population with \(N\) units using a probability proportional to size without replacement (PPSWOR) sampling design based on \(P = (p_ 1,\dots,p_ N)\), \(\Sigma p_ i = 1\). Let \(\pi_ i\) be the probability of including the \(i\)th unit in the sample. In general, for any subset \(s\) of the \(N\) units let \(\pi(s)\) denote the probability of including \(s\) in the sample. This paper gives some order relations between the \(p_ i\), \(\pi_ i\), and \(\pi(s)\). For example, if for any \(i\) and \(j\), \(p_ i \geq p_ j\), then \(\pi_ i\geq\pi_ j\) and conversely. Some interesting bounds on the inclusion probabilities in terms of the selection probabilities are also established.
Mathematics Subject Classification ID: 62D05
zbMATH DE Number: 38238
zbMATH Keywords: unequal probability sampling
zbMATH Keywords: PPSWOR sampling
zbMATH Keywords: probability proportional to size without replacement sampling design
zbMATH Keywords: order relations
zbMATH Keywords: finite population
zbMATH Keywords: bounds
zbMATH Keywords: inclusion probabilities
zbMATH Keywords: selection probabilities
reviewed by: Chien-Pai Han
MaRDI profile type: Publication
cites work: Estimation of Finite Population Properties When Sampling is Without Replacement and Proportional to Magnitude
cites work: On the sampling system with probability proportionate to sum of sizes
cites work: On two systems of unequal probability sampling without replacement
description: scientific article; zbMATH DE number 38238