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Improved parameter estimation of the log-logistic distribution with applications

Author

Listed:
  • Joseph Reath

    (Michigan Technological University)

  • Jianping Dong

    (Michigan Technological University)

  • Min Wang

    (Michigan Technological University)

Abstract

In this paper, we deal with parameter estimation of the log-logistic distribution. It is widely known that the maximum likelihood estimators (MLEs) are usually biased in the case of the finite sample size. This motivates a study of obtaining unbiased or nearly unbiased estimators for this distribution. Specifically, we consider a certain ‘corrective’ approach and Efron’s bootstrap resampling method, which both can reduce the biases of the MLEs to the second order of magnitude. As a comparison, the commonly used generalized moments method is also considered for estimating parameters. Monte Carlo simulation studies are conducted to compare the performances of the various estimators under consideration. Finally, two real-data examples are analyzed to illustrate the potential usefulness of the proposed estimators, especially when the sample size is small or moderate.

Suggested Citation

  • Joseph Reath & Jianping Dong & Min Wang, 2018. "Improved parameter estimation of the log-logistic distribution with applications," Computational Statistics, Springer, vol. 33(1), pages 339-356, March.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0738-y
    DOI: 10.1007/s00180-017-0738-y
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    References listed on IDEAS

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    1. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
    2. Jacob Schwartz & David E. Giles, 2011. "Biased-Reduced Maximum Likelihood Estimation for the Zero-Inflated Poisson Distribution," Econometrics Working Papers 1102, Department of Economics, University of Victoria.
    3. David E. Giles & Hui Feng & Ryan T. Godwin, 2016. "Bias-corrected maximum likelihood estimation of the parameters of the generalized Pareto distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(8), pages 2465-2483, April.
    4. Jacob Schwartz & David E. Giles, 2016. "Bias-reduced maximum likelihood estimation of the zero-inflated Poisson distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(2), pages 465-478, January.
    5. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
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    Cited by:

    1. Ranjita Pandey & Pulkit Srivastava & Neera Kumari, 2021. "On some inferential aspects of length biased log-logistic model," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(1), pages 154-163, February.
    2. Markus Kreer & Ayşe Kızılersü & Jake Guscott & Lukas Christopher Schmitz & Anthony W. Thomas, 2024. "Maximum likelihood estimation for left-truncated log-logistic distributions with a given truncation point," Statistical Papers, Springer, vol. 65(9), pages 5409-5445, December.
    3. 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.
    4. Lucas David Ribeiro-Reis, 2023. "The Log-Logistic Regression Model Under Censoring Scheme," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-12, June.
    5. Abdisalam Hassan Muse & Samuel M. Mwalili & Oscar Ngesa, 2021. "On the Log-Logistic Distribution and Its Generalizations: A Survey," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-93, June.
    6. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.

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