On the Estimation of the Distribution Function Using Extreme and Median Ranked Set Samples

Hani M. Samawi; Omar A.M. Al-Sagheer

doi:10.1002/1521-4036(200106)43:3<357::AID-BIMJ357>3.0.CO;2-Q

On the Estimation of the Distribution Function Using Extreme and Median Ranked Set Samples

Hani M. Samawi, Omar A.M. Al-Sagheer

Biostatistics, Epidemiology & Environmental Health Sciences

Yarmouk University

Research output: Contribution to journal › Article › peer-review

67 Scopus citations

Abstract

 We study relationships between extreme ranked set samples (ERSSs) and median ranked set sample (MRSS) with simple random sample (SRS). For a random variable X, we show that the distribution function estimator when using ERSSs and MRSS are more efficient than when using SRS and ranked set sampling for some values of a given x.
 
 It is shown that using ERSSs can reduce the necessary sample size by a factor of 1.33 to 4 when estimating the median of the distribution. Asymptotic results for the estimation of the distribution function is given for the center of the distribution function. Data on the bilirubin level of babies in neonatal intensive care is used to illustrate the method.

Original language	American English
Pages (from-to)	357-373
Number of pages	17
Journal	Biometrical Journal
Volume	43
Issue number	3
DOIs	https://doi.org/10.1002/1521-4036(200106)43:3<357::AID-BIMJ357>3.0.CO;2-Q
State	Published - Jun 2001

Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty

Disciplines

Biostatistics

Keywords

Distribution function estimation
Extreme ranked set samples
Inference
Median ranked set sample
Ranked set sampling

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10.1002/1521-4036(200106)43:3<357::AID-BIMJ357>3.0.CO;2-QLicense: Unspecified

Cite this

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title = "On the Estimation of the Distribution Function Using Extreme and Median Ranked Set Samples",

abstract = " We study relationships between extreme ranked set samples (ERSSs) and median ranked set sample (MRSS) with simple random sample (SRS). For a random variable X, we show that the distribution function estimator when using ERSSs and MRSS are more efficient than when using SRS and ranked set sampling for some values of a given x. It is shown that using ERSSs can reduce the necessary sample size by a factor of 1.33 to 4 when estimating the median of the distribution. Asymptotic results for the estimation of the distribution function is given for the center of the distribution function. Data on the bilirubin level of babies in neonatal intensive care is used to illustrate the method.",

keywords = "Distribution function estimation, Extreme ranked set samples, Inference, Median ranked set sample, Ranked set sampling",

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note = "We study relationships between extreme ranked set samples (ERSSs) and median ranked set sample (MRSS) with simple random sample (SRS). For a random variable X, we show that the distribution function estimator when using ERSSs and MRSS are more efficient than when using SRS and ranked set sampling for some values of a given x.",

year = "2001",

month = jun,

doi = "10.1002/1521-4036(200106)43:3<357::AID-BIMJ357>3.0.CO;2-Q",

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AU - Samawi, Hani M.

AU - Al-Sagheer, Omar A.M.

N1 - We study relationships between extreme ranked set samples (ERSSs) and median ranked set sample (MRSS) with simple random sample (SRS). For a random variable X, we show that the distribution function estimator when using ERSSs and MRSS are more efficient than when using SRS and ranked set sampling for some values of a given x.

PY - 2001/6

Y1 - 2001/6

N2 - We study relationships between extreme ranked set samples (ERSSs) and median ranked set sample (MRSS) with simple random sample (SRS). For a random variable X, we show that the distribution function estimator when using ERSSs and MRSS are more efficient than when using SRS and ranked set sampling for some values of a given x. It is shown that using ERSSs can reduce the necessary sample size by a factor of 1.33 to 4 when estimating the median of the distribution. Asymptotic results for the estimation of the distribution function is given for the center of the distribution function. Data on the bilirubin level of babies in neonatal intensive care is used to illustrate the method.

AB - We study relationships between extreme ranked set samples (ERSSs) and median ranked set sample (MRSS) with simple random sample (SRS). For a random variable X, we show that the distribution function estimator when using ERSSs and MRSS are more efficient than when using SRS and ranked set sampling for some values of a given x. It is shown that using ERSSs can reduce the necessary sample size by a factor of 1.33 to 4 when estimating the median of the distribution. Asymptotic results for the estimation of the distribution function is given for the center of the distribution function. Data on the bilirubin level of babies in neonatal intensive care is used to illustrate the method.

KW - Distribution function estimation

KW - Extreme ranked set samples

KW - Inference

KW - Median ranked set sample

KW - Ranked set sampling

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DO - 10.1002/1521-4036(200106)43:3<357::AID-BIMJ357>3.0.CO;2-Q

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SN - 0323-3847

VL - 43

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EP - 373

JO - Biometrical Journal

JF - Biometrical Journal

IS - 3

ER -

On the Estimation of the Distribution Function Using Extreme and Median Ranked Set Samples

Abstract

Scopus Subject Areas

Disciplines

Keywords

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