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

Author

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  • Heba F. Nagy

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

  • Amer Ibrahim Al-Omari

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

  • Amal S. Hassan

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

  • Ghadah A. Alomani

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

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.

Suggested Citation

  • Heba F. Nagy & Amer Ibrahim Al-Omari & Amal S. Hassan & Ghadah A. Alomani, 2022. "Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data," Mathematics, MDPI, vol. 10(21), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4102-:d:962468
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    References listed on IDEAS

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    Cited by:

    1. Safar M. Alghamdi & Rashad A. R. Bantan & Amal S. Hassan & Heba F. Nagy & Ibrahim Elbatal & Mohammed Elgarhy, 2022. "Improved EDF-Based Tests for Weibull Distribution Using Ranked Set Sampling," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    2. Jorge Figueroa-Zúñiga & Juan G. Toledo & Bernardo Lagos-Alvarez & Víctor Leiva & Jean P. Navarrete, 2023. "Inference Based on the Stochastic Expectation Maximization Algorithm in a Kumaraswamy Model with an Application to COVID-19 Cases in Chile," Mathematics, MDPI, vol. 11(13), pages 1-14, June.

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