Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data

Nagy, Heba F.; Al-Omari, Amer Ibrahim; Hassan, Amal S.; Alomani, Ghadah A.

doi:10.3390/math10214102

Open AccessArticle

Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data

¹

Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt

²

Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, Jordan

³

Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

^*

Authors to whom correspondence should be addressed.

Mathematics 2022, 10(21), 4102; https://doi.org/10.3390/math10214102

Submission received: 16 September 2022 / Revised: 17 October 2022 / Accepted: 31 October 2022 / Published: 3 November 2022

(This article belongs to the Special Issue Functional Data Analysis: Theory and Applications to Different Scenarios)

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Abstract

The ranked set sampling (RSS) methodology is an effective technique of acquiring data when measuring the units in a population is costly, while ranking them is easy according to the variable of interest. In this article, we deal with an RSS-based estimation of the inverted Kumaraswamy distribution parameters, which is extensively applied in life testing and reliability studies. Some estimation techniques are regarded, including the maximum likelihood, the maximum product of spacing’s, ordinary least squares, weighted least squares, Cramer–von Mises, and Anderson–Darling. We demonstrate a simulation investigation to assess the performance of the suggested RSS-based estimators via accuracy measures relative to simple random sampling. On the basis of actual data regarding the waiting times between 65 consecutive eruptions of Kiama Blowhole, additional conclusions have been drawn. The outcomes of simulation and real data application demonstrated that RSS-based estimators outperformed their simple random sampling counterparts significantly based on the same number of measured units.

Keywords: ranked set sampling; inverted Kumaraswamy distribution; maximum product spacing; maximum likelihood; Cramer–von Mises

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MDPI and ACS Style

Nagy, H.F.; Al-Omari, A.I.; Hassan, A.S.; Alomani, G.A. Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data. Mathematics 2022, 10, 4102. https://doi.org/10.3390/math10214102

AMA Style

Nagy HF, Al-Omari AI, Hassan AS, Alomani GA. Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data. Mathematics. 2022; 10(21):4102. https://doi.org/10.3390/math10214102

Chicago/Turabian Style

Nagy, Heba F., Amer Ibrahim Al-Omari, Amal S. Hassan, and Ghadah A. Alomani. 2022. "Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data" Mathematics 10, no. 21: 4102. https://doi.org/10.3390/math10214102

APA Style

Nagy, H. F., Al-Omari, A. I., Hassan, A. S., & Alomani, G. A. (2022). Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data. Mathematics, 10(21), 4102. https://doi.org/10.3390/math10214102

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Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data

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