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Efficient and Robust Fitting of Lognormal Distributions

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  • Robert Serfling

Abstract

In parametric modeling of loss distributions in actuarial science, a versatile choice with intermediate tail weight is the lognormal distribution. Surprisingly, however, the fitting of this model using estimators that are at once efficient and robust has not been seriously addressed in the extensive literature. Consequently, typical estimators of the lognormal mean and variance fail to be both efficient and robust. In particular, the highly efficient maximum likelihood estimators lack robustness because of their limited sensitivity to outliers in the sample. For the two-parameter lognormal estimation problem, the author considers the problem of efficient and robust joint estimation of the mean and variance of a normal model. He introduces generalized-median-type estimators that yield efficient and robust estimators of various parameters of interest in the lognormal model. The paper provides detailed treatment of the lognormal mean and discusses extension of the approach to the much more complicated problem of estimation for the three-parameter lognormal model.

Suggested Citation

  • Robert Serfling, 2002. "Efficient and Robust Fitting of Lognormal Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(4), pages 95-109.
  • Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:95-109
    DOI: 10.1080/10920277.2002.10596067
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    Cited by:

    1. Fung, Tsz Chai, 2022. "Maximum weighted likelihood estimator for robust heavy-tail modelling of finite mixture models," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 180-198.
    2. Asimit, Alexandru V. & Badescu, Alexandru M. & Verdonck, Tim, 2013. "Optimal risk transfer under quantile-based risk measurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 252-265.
    3. Aaron Clauset & Maxwell Young & Kristian Skrede Gleditsch, 2007. "On the Frequency of Severe Terrorist Events," Journal of Conflict Resolution, Peace Science Society (International), vol. 51(1), pages 58-87, February.
    4. J. D. Opdyke, 2014. "Estimating Operational Risk Capital with Greater Accuracy, Precision, and Robustness," Papers 1406.0389, arXiv.org, revised Nov 2014.
    5. Kundan Singh & Amulya Kumar Mahto & Yogesh Mani Tripathi & Liang Wang, 2024. "Estimation in a multicomponent stress-strength model for progressive censored lognormal distribution," Journal of Risk and Reliability, , vol. 238(3), pages 622-642, June.
    6. N. Balakrishnan & Helton Saulo & Marcelo Bourguignon & Xiaojun Zhu, 2017. "On moment-type estimators for a class of log-symmetric distributions," Computational Statistics, Springer, vol. 32(4), pages 1339-1355, December.
    7. Muhammad Aslam Mohd Safari & Nurulkamal Masseran & Muhammad Hilmi Abdul Majid, 2020. "Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach," Mathematics, MDPI, vol. 8(9), pages 1-21, September.
    8. Brazauskas, Vytaras, 2003. "Influence functions of empirical nonparametric estimators of net reinsurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 115-133, February.
    9. Zhou, Weihua & Serfling, Robert, 2008. "Generalized multivariate rank type test statistics via spatial U-quantiles," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 376-383, March.

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