Environmental and Ecological Statistics

, Volume 6, Issue 1, pp 59–74 | Cite as

Ranked set sample design for environmental investigations

  • Vic Barnett


Ranked set sampling can provide an efficient basis for estimating parameters of environmental variables, particularly when sampling costs are intrinsically high. Various ranked set estimators are considered for the population mean and contrasted in terms of their efficiencies and useful- ness, with special concern for sample design considerations. Specifically, we consider the effects of the form of the underlying random variable, optimisation of efficiency and how to allocate sampling effort for best effect (e.g. one large sample or several smaller ones of the same total size). The various prospects are explored for two important positively skew random variables (lognormal and extreme value) and explicit results are given for these cases. Whilst it turns out that the best approach is to use the largest possible single sample and the optimal ranked set best linear estimator (ranked set BLUE), we find some interesting qualitatively different conclusions for the two skew distributions

Ranked set best linear estimator allocation of sampling effort lognormal distribution extreme value distribution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Balakrishnan, N. and Chan, P.S. (1992) Order statistics from extreme value distribution, I: Tables of means, variances and covariances, Communications in Statistics — Simulation and Computation, 21, 1199-1217Google Scholar
  2. Barnett, V. and Moore, K.L. (1997) Best linear unbiased estimates in ranked set sampling with particular reference to imperfect ordering, Journal of Applied Statistics, 24, 699-710Google Scholar
  3. Bhoj, D.S. (1997) Estimation of parameters of the extreme value distribution using ranked set sampling Commnunications in Statistics — Theory and Methods, 26, 653-667Google Scholar
  4. Gupta, S.S.; McDonald, G.C. and Galarneau, D.I. (1974) Moments product moments and percentage points of the order statistics from the lognormal distribution for samples of size twenty and less, Sankhya B, 36, 230-260.Google Scholar
  5. McIntyre, G. (1952) A method of unbiased selective sampling, using ranked sets, Australian Journal of Agricultural Research, 3, 385-390.Google Scholar
  6. Johnson, N.L.; Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, Vol 2, Wiley, New York.Google Scholar
  7. Kaur, A.; Patil, G.P. and Taillie, C. (1997) Unequal allocation models for ranked set sampling with skew distributions, Biometrics, 53, 123-130Google Scholar
  8. Lieblein, J. and Zelen, M. (1956) Statistical investigations of the fatigue life of deep-groove ball bearings, Journal of Research, National Bureau of Standards., 57, 273-315.Google Scholar
  9. Patil, G.P. (1991) Encountered data, statistical ecology, environmental statistics, and weight-distributed methods. Technical Report No. 91-0725. Center for Statistical Ecology and Environmental Statistics, Penn State University, US.Google Scholar
  10. Shen, W-H. (1994) On estimation of a lognormal mean using a ranked set sample, Sankhya, 56, 323-333.Google Scholar
  11. Sinha, B.K.; Sinha, R.K. and Purkayastha, S. (1995) On some aspects of ranked set sampling for estimation of normal and exponential parameters, Statistical Decisions, 14, 223-240.Google Scholar
  12. Stokes, S.L. (1995) Parametric ranked set sampling Annals of the Institute of Statistical Mathematics, 47, 465-482.Google Scholar
  13. Webster, R. and Oliver, M.A. (1990) Statistical Methods in Soil and Land Resource Survey, OUP, Oxford.Google Scholar
  14. White, J.S. (1969) The moments of log-Weibull order statistics, Technometrics, 11, 373-386.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Vic Barnett
    • 1
  1. 1.University of NottinghamUK

Personalised recommendations