Estimation methods based on ranked set sampling for the arctan uniform distribution with application

Salem A. Alyami; Amal S. Hassan; Ibrahim Elbatal; Naif Alotaibi; Ahmed M. Gemeay; Mohammed Elgarhy; Salem A. Alyami; Amal S. Hassan; Ibrahim Elbatal; Naif Alotaibi; Ahmed M. Gemeay; Mohammed Elgarhy

doi:10.3934/math.2024504

AIMS Mathematics

2024, Volume 9, Issue 4: 10304-10332. doi: 10.3934/math.2024504

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Estimation methods based on ranked set sampling for the arctan uniform distribution with application

1.
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia
2.
Faculty of Graduate Studies for Statistical Research, Cairo University, 5 Dr. Ahmed Zewail Street, Giza, 12613, Egypt
3.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
4.
Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef, 62521, Egypt
5.
Department of Basic Sciences, Higher Institute for Administrative Sciences, Belbeis, AlSharkia, Egypt

Received: 26 November 2023 Revised: 07 January 2024 Accepted: 17 January 2024 Published: 14 March 2024
MSC : 62F15, 62G20, 65C60

The arctan uniform distribution (AUD) is a brand-new bounded distribution that may be used for modeling a variety of existing bounded real-world datasets. Ranked set sampling (RSS) is a useful technique for parameter estimation when accurate measurement of the observation is challenging and/or expensive. In the current study, the parameter estimator of the AUD is addressed based on RSS and simple random sampling (SRS) techniques. Some of the popular conventional estimating techniques are considered. The efficiency of the produced estimates is compared using a Monte Carlo simulation. It appears that the maximum product spacing method has an advantage in assessing the quality of proposed estimates based on the outcomes of our simulations for both the SRS and RSS datasets. In comparison to estimates produced from the SRS datasets, it can be seen that those from the RSS datasets are more reliable. This implies that RSS is a more effective sampling technique in terms of generating estimates with a smaller mean squared error. The benefit of the RSS design over the SRS design is further supported by real data results.
- ranked set sampling,
- arctan uniform distribution,
- mean absolute relative error
Citation: Salem A. Alyami, Amal S. Hassan, Ibrahim Elbatal, Naif Alotaibi, Ahmed M. Gemeay, Mohammed Elgarhy. Estimation methods based on ranked set sampling for the arctan uniform distribution with application[J]. AIMS Mathematics, 2024, 9(4): 10304-10332. doi: 10.3934/math.2024504

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Abstract

The arctan uniform distribution (AUD) is a brand-new bounded distribution that may be used for modeling a variety of existing bounded real-world datasets. Ranked set sampling (RSS) is a useful technique for parameter estimation when accurate measurement of the observation is challenging and/or expensive. In the current study, the parameter estimator of the AUD is addressed based on RSS and simple random sampling (SRS) techniques. Some of the popular conventional estimating techniques are considered. The efficiency of the produced estimates is compared using a Monte Carlo simulation. It appears that the maximum product spacing method has an advantage in assessing the quality of proposed estimates based on the outcomes of our simulations for both the SRS and RSS datasets. In comparison to estimates produced from the SRS datasets, it can be seen that those from the RSS datasets are more reliable. This implies that RSS is a more effective sampling technique in terms of generating estimates with a smaller mean squared error. The benefit of the RSS design over the SRS design is further supported by real data results.

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