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Estimation of Location and Scale Parameters of a Logistic Distribution Using a Ranked Set Sample

In: Statistical Theory and Applications

Author

Listed:
  • Kin Lam
  • Bimal K. Sinha
  • Zhong Wu

Abstract

In situations where the experimental or sampling units in a study can be more easily ranked than quantified, McIntyre (1952) proposed that the mean of n units based on a ranked set sample (RSS) be used to estimate the population mean. He observed that it provides an unbiased estimator with a smaller variance compared to the mean of a simple random sample (SRS) of the same size n. McIntyre’s concept of RSS is essentially nonparametric in nature in that the underlying population distribution is assumed to be completely unknown. Here we explore the concept of RSS to estimate the location, scale and quantiles of a logistic distribution. It turns out that the use of RSS and its suitable modifications result in much improved estimators compared to the use of an SRS in all the three cases.

Suggested Citation

  • Kin Lam & Bimal K. Sinha & Zhong Wu, 1996. "Estimation of Location and Scale Parameters of a Logistic Distribution Using a Ranked Set Sample," Springer Books, in: H. N. Nagaraja & Pranab Kumar Sen & Donald F. Morrison (ed.), Statistical Theory and Applications, chapter 16, pages 187-197, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3990-1_16
    DOI: 10.1007/978-1-4612-3990-1_16
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