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Parameter estimation of exponentiated exponential distribution under selective ranked set sampling

Author

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  • Hassan Amal S.

    (Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Egypt .)

  • Elshaarawy Rasha S.

    (Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Egypt .)

  • Nagy Heba F.

    (Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Egypt .)

Abstract

Partial ranked set sampling (PRSS) is a cost-effective sampling method. It is a combination of simple random sample (SRS) and ranked set sampling (RSS) designs. The PRSS method allows flexibility for the experimenter in selecting the sample when it is either difficult to rank the units within each set with full confidence or when experimental units are not available. In this article, we introduce and define the likelihood function of any probability distribution under the PRSS scheme. The performance of the maximum likelihood estimators is examined when the available data are assumed to have an exponentiated exponential (EE) distribution via some selective RSS schemes as well as SRS. The suggested ranked schemes include the PRSS, RSS, neoteric RSS (NRSS), and extreme RSS (ERSS). An intensive simulation study was conducted to compare and explore the behaviour of the proposed estimators. The study demonstrated that the maximum likelihood estimators via PRSS, NRSS, ERSS, and RSS schemes are more efficient than the corresponding estimators under SRS. A real data set is presented for illustrative purposes.

Suggested Citation

  • Hassan Amal S. & Elshaarawy Rasha S. & Nagy Heba F., 2022. "Parameter estimation of exponentiated exponential distribution under selective ranked set sampling," Statistics in Transition New Series, Statistics Poland, vol. 23(4), pages 37-58, December.
    • Handle: RePEc:vrs:stintr:v:23:y:2022:i:4:p:37-58:n:12
    DOI: 10.2478/stattrans-2022-0041
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    References listed on IDEAS

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    1. M. A. Sabry & M. Shaaban, 2020. "Dependent Ranked Set Sampling Designs for Parametric Estimation with Applications," Annals of Data Science, Springer, vol. 7(2), pages 357-371, June.
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    4. Walid Abu-Dayyeh & Aissa Assrhani & Kamarulzaman Ibrahim, 2013. "Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling," Statistical Papers, Springer, vol. 54(1), pages 207-225, February.
    5. Abdul Haq & Jennifer Brown & Elena Moltchanova & Amer Ibrahim Al‐Omari, 2013. "Partial ranked set sampling design," Environmetrics, John Wiley & Sons, Ltd., vol. 24(3), pages 201-207, May.
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