Empirical distribution function estimators based on sampling designs in a finite population using single auxiliary variable

Yildiz, Tuğba Özkal; Sevil, Yusuf Can

doi:10.1080/02664763.2019.1625311

Cited by 2 publications

(3 citation statements)

References 17 publications

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“…Recently, statistical inference for mean, total, variance and quantiles have been discussed by Ozturk [25,26,27], Ozturk and Bayramoglu Kavlak [28,29] in finite population setting. Also, Sevil and Yildiz [30,31] and Yildiz and Sevil [32,33] proposed the following empirical distribution function (EDF) in finite population setting.…”

Section: Introductionmentioning

confidence: 99%

“…They proved that the EDF is unbiased and is more efficient than the EDF based on SRS. Moreover, the EDFs based on the sampling designs was applied to air quality data by Yildiz and Sevil [33] and to body mass index by Sevil and Yildiz [31]. Ozturk et al [34] showed that the procedure of RSS can be used to collect data from farm animals, such as sheep, cattle and cows.…”

Section: Introductionmentioning

confidence: 99%

“…If the distribution function of the sheep weights is estimated, both the quantiles and the probabilities corresponding to the specific quantiles can be obtained. Unlike the studies Sevil and Yildiz [30,31] and Yildiz and Sevil [32,33], we provide design-based estimators for distribution function. These estimators use the information of inclusion probabilities as well.…”

Section: Introductionmentioning

confidence: 99%

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Design-based estimators of distribution function in ranked set sampling with an application

Sevil,

Yildiz

2022

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Empirical distribution functions (EDFs) based on ranked set sampling (RSS) and its modifications have been examined by many authors. In these studies, the proposed estimators have been investigated for infinite population setting. However, developing EDF estimators in finite population setting would be more valuable for areas such as environmental, ecological, agricultural, biological, etc. This paper introduces new EDF estimators based on level-0, level-1 and level-2 sampling designs in RSS. Asymptotic properties of the new EDF estimators have been established. Numerical results have been obtained for the case when ranking is imperfect under different distribution functions. It has been observed that level-2 sampling design provides more efficient EDF estimator than its counterparts of level-0, level-1 and simple random sampling. In real data application, we consider a pointwise estimate of distribution function and estimation of the median of sheep's weights at seven months using RSS based on level-2 sampling design.

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