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

Article

Abstract

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.

Keywords

Allocation rules Concomitant variables Multiple characteristics Relative precision Skewness 

Abbreviations

RSS

Ranked set sampling

SRS

Simple random sampling

SD

Standard deviation

CV

Coefficient of variation

FSS

Farm Structure Survey

UDE

European size unit

SAU

Utilized agricultural surface

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References

  1. Al-Saleh MF, Zheng G (2002) Estimation of bivariate characteristics using ranked set sampling. Aust N Z J Stat 44: 221–232. doi:10.1111/1467-842X.00224 CrossRefGoogle Scholar
  2. Dell TR, Clutter JL (1972) Ranked set sampling theory with other statistics background. Biometrics 28: 545–555. doi:10.2307/2556166 CrossRefGoogle Scholar
  3. Husby CE, Stasny EA, Wolfe DA (2005) An application of ranked set sampling for mean and median estimation using USDA crop production data. J Agric Biol Environ Stat 10: 354–373. doi:10.1198/108571105X58234 CrossRefGoogle Scholar
  4. Kaur A, Patil GP, Taillie C (1997) Unequal allocation models for ranked set sampling with skew distributions. Biometrics 53: 123–130. doi:10.2307/2533102 CrossRefGoogle Scholar
  5. Kish L (1965) Survey sampling. Wiley, New YorkGoogle Scholar
  6. McIntyre GA (1952) A method of unbiased selective sampling, using ranked sets. Aust J Agric Res 3: 385–390. doi:10.1071/AR9520385 CrossRefGoogle Scholar
  7. Norris RC, Patil GP, Sinha AK (1995) Estimation of multiple characteristics by ranked set sampling. Coenoses 10(2–3): 95–111Google Scholar
  8. Ridout MS (2003) On ranked set sampling for multiple characteristics. Environ Ecol Stat 10: 255–262. doi:10.1023/A:1023694729011 CrossRefGoogle Scholar
  9. Stokes SL (1977) Ranked set sampling with concomitant variables. Commun Stat Theory Methods A 6: 1207–1211. doi:10.1080/03610927708827563 CrossRefGoogle Scholar

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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