### Abstract

Precision of the estimate of the population mean using ranked set sample (RSS) relative to using simple random sample (SRS), with the same number of quantified units, depends upon the population and success in ranking. In practice, even ranking a sample of moderate size and observing the ith ranked unit (other than the extremes) is a difficult task. Therefore, in this paper we introduce a variety of extreme ranked set sample (ERSS_{s}) to estimate the population mean ERSS_{s} is more practical than the ordinary ranked set sampling, since in case of even sample size we need to identify successfully only the first and/or the last ordered unit or in case of odd sample size the median unit. We show that ERSS_{s} gives an unbiased estimate of the population mean in case of symmetric populations and it is more efficient than SRS, using the same number of quantified units. Example using real data is given. Also, parametric examples are given.

Original language | English |
---|---|

Pages (from-to) | 577-586 |

Number of pages | 10 |

Journal | Biometrical Journal |

Volume | 38 |

Issue number | 5 |

Publication status | Published - 1996 |

### Fingerprint

### Keywords

- Extreme ranked set sample
- Mean square error
- Order statistics
- Ranked set sample
- Simple random sample

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Biometrical Journal*,

*38*(5), 577-586.

**Estimating the population mean using extreme ranked set sampling.** / Samawi, Hani Michel; Ahmed, Mohammad S.; Abu-Dayyeh, Walid.

Research output: Contribution to journal › Article

*Biometrical Journal*, vol. 38, no. 5, pp. 577-586.

}

TY - JOUR

T1 - Estimating the population mean using extreme ranked set sampling

AU - Samawi, Hani Michel

AU - Ahmed, Mohammad S.

AU - Abu-Dayyeh, Walid

PY - 1996

Y1 - 1996

N2 - Precision of the estimate of the population mean using ranked set sample (RSS) relative to using simple random sample (SRS), with the same number of quantified units, depends upon the population and success in ranking. In practice, even ranking a sample of moderate size and observing the ith ranked unit (other than the extremes) is a difficult task. Therefore, in this paper we introduce a variety of extreme ranked set sample (ERSSs) to estimate the population mean ERSSs is more practical than the ordinary ranked set sampling, since in case of even sample size we need to identify successfully only the first and/or the last ordered unit or in case of odd sample size the median unit. We show that ERSSs gives an unbiased estimate of the population mean in case of symmetric populations and it is more efficient than SRS, using the same number of quantified units. Example using real data is given. Also, parametric examples are given.

AB - Precision of the estimate of the population mean using ranked set sample (RSS) relative to using simple random sample (SRS), with the same number of quantified units, depends upon the population and success in ranking. In practice, even ranking a sample of moderate size and observing the ith ranked unit (other than the extremes) is a difficult task. Therefore, in this paper we introduce a variety of extreme ranked set sample (ERSSs) to estimate the population mean ERSSs is more practical than the ordinary ranked set sampling, since in case of even sample size we need to identify successfully only the first and/or the last ordered unit or in case of odd sample size the median unit. We show that ERSSs gives an unbiased estimate of the population mean in case of symmetric populations and it is more efficient than SRS, using the same number of quantified units. Example using real data is given. Also, parametric examples are given.

KW - Extreme ranked set sample

KW - Mean square error

KW - Order statistics

KW - Ranked set sample

KW - Simple random sample

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UR - http://www.scopus.com/inward/citedby.url?scp=0030490310&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030490310

VL - 38

SP - 577

EP - 586

JO - Biometrical Journal

JF - Biometrical Journal

SN - 0323-3847

IS - 5

ER -