Manipulation-based ranked set sampling scheme

Azhar Mehmood Abbasi, Muhammad Yousaf Shahd

Abstract


Cost-effective and efficient sampling methods are of main concern in many social, biological and environmental studies. In this article, an efficient sampling scheme, named manipulation-based ranked set sampling (MBRSS) scheme is introduced with its properties for estimating population mean and median. The MBRSS is a mixture of simple random sampling (SRS), ranked set sampling (RSS) and median ranked set sampling (MRSS) schemes and is applicable in the situation when ordinary RSS cannot be conducted. It is shown that the proposed scheme provides unbiased mean estimator provided underlying distribution is symmetric. For asymmetric distributions, a weighted mean is proposed, where optimal weights are computed using Shannon's entropy. Monte Carlo simulation is used to ascertain effectiveness of the proposed mean and median estimators in the presence of outliers. We also compared the efficiency of MBRSS and truncation-based ranked set sampling (TBRSS) scheme with respect to SRS under the situation of perfect and imperfect ranking i.e error in rankings with respect to variable of interest. It is observed, on the basis of theoretical and numerical studies that MBRSS is more efficient than SRS. Further, a real data set is used to illustrate the proposed MBRSS scheme.

Keywords


simple random sample, ranked set sampling, median ranked set sampling, truncation-based ranked set sampling, perfect ranking, imperfect ranking.

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DOI: http://dx.doi.org/10.18187/pjsor.v13i4.1539

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Title

Manipulation-based ranked set sampling scheme

Keywords

simple random sample, ranked set sampling, median ranked set sampling, truncation-based ranked set sampling, perfect ranking, imperfect ranking.

Description

Cost-effective and efficient sampling methods are of main concern in many social, biological and environmental studies. In this article, an efficient sampling scheme, named manipulation-based ranked set sampling (MBRSS) scheme is introduced with its properties for estimating population mean and median. The MBRSS is a mixture of simple random sampling (SRS), ranked set sampling (RSS) and median ranked set sampling (MRSS) schemes and is applicable in the situation when ordinary RSS cannot be conducted. It is shown that the proposed scheme provides unbiased mean estimator provided underlying distribution is symmetric. For asymmetric distributions, a weighted mean is proposed, where optimal weights are computed using Shannon's entropy. Monte Carlo simulation is used to ascertain effectiveness of the proposed mean and median estimators in the presence of outliers. We also compared the efficiency of MBRSS and truncation-based ranked set sampling (TBRSS) scheme with respect to SRS under the situation of perfect and imperfect ranking i.e error in rankings with respect to variable of interest. It is observed, on the basis of theoretical and numerical studies that MBRSS is more efficient than SRS. Further, a real data set is used to illustrate the proposed MBRSS scheme.

Date

2017-12-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 13 No. 4, 2017



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810