Environmental and Ecological Statistics

, Volume 17, Issue 3, pp 333–345 | Cite as

Ranked set sampling allocation models for multiple skewed variables: an application to agricultural data



The mean of a balanced ranked set sample is more efficient than the mean of a simple random sample of equal size and the precision of ranked set sampling may be increased by using an unbalanced allocation when the population distribution is highly skewed. The aim of this paper is to show the practical benefits of the unequal allocation in estimating simultaneously the means of more skewed variables through real data. In particular, the allocation rule suggested in the literature for a single skewed distribution may be easily applied when more than one skewed variable are of interest and an auxiliary variable correlated with them is available. This method can lead to substantial gains in precision for all the study variables with respect to the simple random sampling, and to the balanced ranked set sampling too.


Allocation rules Concomitant variables Multiple characteristics Relative precision Skewness 



Ranked set sampling


Simple random sampling


Standard deviation


Coefficient of variation


Farm Structure Survey


European size unit


Utilized agricultural surface


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Chiara Bocci
    • 1
  • Alessandra Petrucci
    • 1
  • Emilia Rocco
    • 1
  1. 1.Department of Statistics “G. Parenti”University of FlorenceFlorenceItaly

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