Abstract
In this article, quartile double ranked set sampling (QDRSS) method is considered for estimating the population median. The sample median based on QDRSS is suggested as an estimator of the population median. The QDRSS is compared with the simple random sampling (SRS), ranked set sampling (RSS) and quartile ranked set sampling (QRSS) methods. A real data set is used for illustration. It turns out that, for the symmetric distributions considered in this study, the QDRSS estimators are unbiased of the population median and are more than their counterparts using SRS, RSS and QRSS based on the same sample number of measured units. For asymmetric distributions, QDRSS is biased and it is more efficient than SRS, QRSS for all sample size m while it is more efficient than RSS if m>4 .
Highlights
Ranked set sampling was first suggested by McIntyre (1952) as a cost efficient sampling procedure when compared to the commonly used simple random sampling in situations where visual ordering of set units can be done but the exact measurement of the units is difficult and expensive
Are, respectively, 6.568 and 3.334 for estimating the median of standard normal distribution. This may be due to that: in the case of odd sample size we select only the median of the set of the rank i m 1, while with even sample size we identify the first or the third 2 quartile of the ith sample
quartile double ranked set sampling (QDRSS) is more efficient than ranked set sampling (RSS)
Summary
Ranked set sampling was first suggested by McIntyre (1952) as a cost efficient sampling procedure when compared to the commonly used simple random sampling in situations where visual ordering of set units can be done but the exact measurement of the units is difficult and expensive. Muttlak (1997) suggested median ranked set sampling for estimating the population mean. Al-Saleh and Al-Kadiri (2000) considered double ranked set sampling (DRSS) method for estimating the population mean, and they showed that the ranking at the second stage is easier than the ranking at the first stage. Al-Saleh and Al-Omari (2002) generalized the DRSS to multistage ranked set sampling to increase the efficiency of the estimators for specific value of the sample size. AlOmari and Al-Saleh (2009) suggested quartile double ranked set sampling (QDRSS) for estimating the population mean. Al-Omari (2010) suggested an estimator of the population median using double robust extreme ranked set sampling. Entropy estimation and goodnessof-fit tests for the inverse Gaussian and Laplace distributions using paired ranked set sampling method is suggested by Al-Omari and Haq (2015). For more about RSS and its modifications see Sinha et al (2006), Ozturk and Jozani (2014), Hatefi et al (2014), Samawi and Al-Saleh (2014), Bouza (2002), and Tiwari and Pandey (2013)
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