This paper proposes an adjustment method to overcome the difficulties encountered by the maximum likelihood method in the case of the three-parameter lognormal distribution. Endeed, when the threshold parameter is close to the smallest order statistic, the standard likelihood function is no longer bounded. In this case, maximum likelihood estimators are no longer accessible. Our strategy is twofold: first, we construct adaptive bounds intended to contain the location and shape parameters with a probability close to one as the sample size increases. Second, we construct a marginal likelihood function, which we maximize using an optimization method available in the R software through the ”nlnimb” package. This likelihood function is based on the (n-1) largest order statistics. Finally, Monte Carlo simulation studies are used to analyze the asymptotic behavior of the constructed intervals and to study the asymptotic properties of the proposed estimators through bias and the Root Mean-Squared Error(RMSE).
| Published in | Mathematics and Computer Science (Volume 11, Issue 1) |
| DOI | 10.11648/j.mcs.20261101.11 |
| Page(s) | 1-5 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Order statistics, Maximum Likelihood Estimation, Left Censored Samples, Three Parameter Lognormal Distribution
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APA Style
Jean-Etienne, O. O., Edoh, K. (2026). Marginalized Maximum Likelihood Estimation Method for the Three-parameter Lognormal Distribution. Mathematics and Computer Science, 11(1), 1-5. https://doi.org/10.11648/j.mcs.20261101.11
ACS Style
Jean-Etienne, O. O.; Edoh, K. Marginalized Maximum Likelihood Estimation Method for the Three-parameter Lognormal Distribution. Math. Comput. Sci. 2026, 11(1), 1-5. doi: 10.11648/j.mcs.20261101.11
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Download@article{10.11648/j.mcs.20261101.11,
author = {Ouedraogo Ouindllassida Jean-Etienne and Katchekpele Edoh},
title = {Marginalized Maximum Likelihood Estimation Method for the Three-parameter Lognormal Distribution
},
journal = {Mathematics and Computer Science},
volume = {11},
number = {1},
pages = {1-5},
doi = {10.11648/j.mcs.20261101.11},
url = {https://doi.org/10.11648/j.mcs.20261101.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20261101.11},
abstract = {This paper proposes an adjustment method to overcome the difficulties encountered by the maximum likelihood method in the case of the three-parameter lognormal distribution. Endeed, when the threshold parameter is close to the smallest order statistic, the standard likelihood function is no longer bounded. In this case, maximum likelihood estimators are no longer accessible. Our strategy is twofold: first, we construct adaptive bounds intended to contain the location and shape parameters with a probability close to one as the sample size increases. Second, we construct a marginal likelihood function, which we maximize using an optimization method available in the R software through the ”nlnimb” package. This likelihood function is based on the (n-1) largest order statistics. Finally, Monte Carlo simulation studies are used to analyze the asymptotic behavior of the constructed intervals and to study the asymptotic properties of the proposed estimators through bias and the Root Mean-Squared Error(RMSE).
},
year = {2026}
}
TY - JOUR T1 - Marginalized Maximum Likelihood Estimation Method for the Three-parameter Lognormal Distribution AU - Ouedraogo Ouindllassida Jean-Etienne AU - Katchekpele Edoh Y1 - 2026/01/15 PY - 2026 N1 - https://doi.org/10.11648/j.mcs.20261101.11 DO - 10.11648/j.mcs.20261101.11 T2 - Mathematics and Computer Science JF - Mathematics and Computer Science JO - Mathematics and Computer Science SP - 1 EP - 5 PB - Science Publishing Group SN - 2575-6028 UR - https://doi.org/10.11648/j.mcs.20261101.11 AB - This paper proposes an adjustment method to overcome the difficulties encountered by the maximum likelihood method in the case of the three-parameter lognormal distribution. Endeed, when the threshold parameter is close to the smallest order statistic, the standard likelihood function is no longer bounded. In this case, maximum likelihood estimators are no longer accessible. Our strategy is twofold: first, we construct adaptive bounds intended to contain the location and shape parameters with a probability close to one as the sample size increases. Second, we construct a marginal likelihood function, which we maximize using an optimization method available in the R software through the ”nlnimb” package. This likelihood function is based on the (n-1) largest order statistics. Finally, Monte Carlo simulation studies are used to analyze the asymptotic behavior of the constructed intervals and to study the asymptotic properties of the proposed estimators through bias and the Root Mean-Squared Error(RMSE). VL - 11 IS - 1 ER -
Science and technology, University of Norbert ZONGO, Koudougou, Burkina Faso
Science and technology, University of Norbert ZONGO, Koudougou, Burkina Faso; Faculty of Science and Technology, University of Kara, Kara, Togo
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