### Abstract

We modify RSS to come up with new sampling method, namely, Multistage Median Ranked Set Sampling (MMRSS). The MMRSS was suggested for estimating the population median and to increase the efficiency of the estimator for specific value of the sample size. The MMRSS was conapared to the Simple Random Sampling (SRS), Ranked Set Sampling (RSS) and Median Ranked Set Sampling (MRSS) methods. It is found that MMRSS gives an unbiased estimate of the population median of symmetric distributions and it is more efficient than SRS, RSS and MRSS based on the same number of measured units. Also, it was found that the efficiency of MMRSS increases in r (r is the number of stage) for specific value of the sample size. For asymmetric distributions considered in this study, MMRSS has a small bias, close to zero as r increases, especially with odd sample-size. A set of real data was used to illustrate the method.

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

Pages (from-to) | 58-64 |

Number of pages | 7 |

Journal | Journal of Mathematics and Statistics |

Volume | 3 |

Issue number | 2 |

Publication status | Published - 2007 |

### Fingerprint

### Keywords

- Median ranked set sampling
- Multistage median ranked set sampling
- Multistage ranked set sampling
- Ranked set sampling
- Simple random sampling

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Journal of Mathematics and Statistics*,

*3*(2), 58-64.

**Multistage median ranked set sampling for estimating the population median.** / Jemain, Abdul Aziz; Al-Omari, Amer; Ibrahim, Kamarulzaman.

Research output: Contribution to journal › Article

*Journal of Mathematics and Statistics*, vol. 3, no. 2, pp. 58-64.

}

TY - JOUR

T1 - Multistage median ranked set sampling for estimating the population median

AU - Jemain, Abdul Aziz

AU - Al-Omari, Amer

AU - Ibrahim, Kamarulzaman

PY - 2007

Y1 - 2007

N2 - We modify RSS to come up with new sampling method, namely, Multistage Median Ranked Set Sampling (MMRSS). The MMRSS was suggested for estimating the population median and to increase the efficiency of the estimator for specific value of the sample size. The MMRSS was conapared to the Simple Random Sampling (SRS), Ranked Set Sampling (RSS) and Median Ranked Set Sampling (MRSS) methods. It is found that MMRSS gives an unbiased estimate of the population median of symmetric distributions and it is more efficient than SRS, RSS and MRSS based on the same number of measured units. Also, it was found that the efficiency of MMRSS increases in r (r is the number of stage) for specific value of the sample size. For asymmetric distributions considered in this study, MMRSS has a small bias, close to zero as r increases, especially with odd sample-size. A set of real data was used to illustrate the method.

AB - We modify RSS to come up with new sampling method, namely, Multistage Median Ranked Set Sampling (MMRSS). The MMRSS was suggested for estimating the population median and to increase the efficiency of the estimator for specific value of the sample size. The MMRSS was conapared to the Simple Random Sampling (SRS), Ranked Set Sampling (RSS) and Median Ranked Set Sampling (MRSS) methods. It is found that MMRSS gives an unbiased estimate of the population median of symmetric distributions and it is more efficient than SRS, RSS and MRSS based on the same number of measured units. Also, it was found that the efficiency of MMRSS increases in r (r is the number of stage) for specific value of the sample size. For asymmetric distributions considered in this study, MMRSS has a small bias, close to zero as r increases, especially with odd sample-size. A set of real data was used to illustrate the method.

KW - Median ranked set sampling

KW - Multistage median ranked set sampling

KW - Multistage ranked set sampling

KW - Ranked set sampling

KW - Simple random sampling

UR - http://www.scopus.com/inward/record.url?scp=34548146291&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548146291&partnerID=8YFLogxK

M3 - Article

VL - 3

SP - 58

EP - 64

JO - Journal of Mathematics and Statistics

JF - Journal of Mathematics and Statistics

SN - 1549-3644

IS - 2

ER -