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Maximum likelihood estimators of the parameters of the log-logistic distribution

Author

Listed:
  • Xiaofang He

    (Jishou University)

  • Wangxue Chen

    (Jishou University)

  • Wenshu Qian

    (Jishou University)

Abstract

In this article, maximum likelihood estimator(s) (MLE(s)) of the scale and shape parameters $$\alpha $$ α and $$\beta $$ β from log-logistic distribution will be respectively considered in cases when one parameter is known and when both are unknown under simple random sampling (SRS) and ranked set sampling (RSS). In addition, the MLE of one parameter, when another parameter is known using a RSS version based on the order statistic that maximizes the Fisher information for a fixed set size, will be considered. These MLEs will be compared in terms of asymptotic efficiencies. These MLEs based on RSS can be real competitors against those based on SRS. All efficiencies of these MLEs are simulated under imperfect ranking.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:5:d:10.1007_s00362-018-1011-3
    DOI: 10.1007/s00362-018-1011-3
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    References listed on IDEAS

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    1. 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.
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    6. 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.
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