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Parametric estimation for the scale parameter for scale distributions using moving extremes ranked set sampling

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  • Chen, Wangxue
  • Xie, Minyu
  • Wu, Ming

Abstract

A modification of ranked set sampling (RSS) called moving extremes ranked set sampling (MERSS) is considered for the estimation of the scale parameter of scale distributions. A maximum likelihood estimator (MLE) is studied and its properties are obtained. We prove the MLE is an equivariant estimator under scale transformation. In order to give more insight into the performance of MERSS with respect to (w.r.t.) simple random sampling (SRS), the asymptotic efficiency of the MLE using MERSS w.r.t. that using SRS is computed for some usual scale distributions. The relative results show that the MLE using MERSS can be real competitors to the MLE using SRS, when the same sample size is used.

Suggested Citation

  • Chen, Wangxue & Xie, Minyu & Wu, Ming, 2013. "Parametric estimation for the scale parameter for scale distributions using moving extremes ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2060-2066.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:9:p:2060-2066
    DOI: 10.1016/j.spl.2013.05.015
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    References listed on IDEAS

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    1. Mohammad Al-Saleh & Said Al-Hadhrami, 2003. "Estimation of the mean of the exponential distribution using moving extremes ranked set sampling," Statistical Papers, Springer, vol. 44(3), pages 367-382, July.
    2. Kin Lam & Bimal Sinha & Zhong Wu, 1994. "Estimation of parameters in a two-parameter exponential distribution using ranked set sample," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 723-736, December.
    3. Lynne Stokes, 1995. "Parametric ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 465-482, September.
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    Cited by:

    1. Amer Ibrahim Al-Omari & SidAhmed Benchiha & Ibrahim M. Almanjahie, 2022. "Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design," Mathematics, MDPI, vol. 10(17), pages 1-18, September.
    2. Wangxue Chen & Rui Yang & Dongsen Yao & Chunxian Long, 2021. "Pareto parameters estimation using moving extremes ranked set sampling," Statistical Papers, Springer, vol. 62(3), pages 1195-1211, June.
    3. Wenshu Qian & Wangxue Chen & Xiaofang He, 2021. "Parameter estimation for the Pareto distribution based on ranked set sampling," Statistical Papers, Springer, vol. 62(1), pages 395-417, February.
    4. Alexey Kudryavtsev & Oleg Shestakov, 2023. "Estimates of the Convergence Rate in the Generalized Rényi Theorem with a Structural Digamma Distribution Using Zeta Metrics," Mathematics, MDPI, vol. 11(21), pages 1-10, October.
    5. Hamid Rahmani & Mostafa Razmkhah, 2017. "Perfect ranking test in moving extreme ranked set sampling," Statistical Papers, Springer, vol. 58(3), pages 855-875, September.
    6. Xiaofang He & Wangxue Chen & Wenshu Qian, 2020. "Maximum likelihood estimators of the parameters of the log-logistic distribution," Statistical Papers, Springer, vol. 61(5), pages 1875-1892, October.

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