Metrika

, Volume 3, Issue 1, pp 53–60 | Cite as

On the efficiency of sampling with varying probabilities and the selection of units with replacement

  • S. S. Zarkovic
Veröffentlichungen

Summary

In this paper the efficiency of sampling with varying probabilities is being compared with the efficiency of some alternative methods, such as simple random sampling, ratio estimate, regression estimate, difference estimate, and stratified sampling with proportionate allocation. The variance formula of the estimated arithmetic mean in the case of sampling with varying probabilities (3) was transformed into (5) and (6) by expanding (3) in Taylor series and the comparisons between the above methods are obtained in Table 1. It was also shown that similar comparisons are possible with multi-stage designs.

Zusammenfassung

Die Wirksamkeit des Stichprobenverfahrens mit veränderlichen Wahrscheinlichkeiten wird verglichen mit der Wirksamkeit einiger anderer Verfahren, u.z. der uneingeschränkten Zufallsauswahl mit einfacher Hochrechnung und bei Verwendung der Verhältnis-, Regressions- und Differenzenschätzung und der geschichteten Auswahl mit proportionaler Aufteilung. Zu diesem Zweck wurde die Formel für die Varianz des geschätzten arithmetischen Mittels im Fall des Verfahrens mit veränderlichen Wahrscheinlichkeiten (3) mithilfe einer Taylor-Entwicklung in (5) und (6) transformiert. Die Ergebnisse des Vergleichs sind in Tabelle 1 gegeben. Abschließend wird gezeigt, daß ähnliche Vergleiche auch mit mehrstufigen Verfahren möglich sind.

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Copyright information

© Physica-Verlag 1960

Authors and Affiliations

  • S. S. Zarkovic
    • 1
  1. 1.Methodology Branch, Statistics Division, Food and Agriculture Organization of the United NationsRomeItaly

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