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Parameter Estimation in a Three-Parameter Lognormal Distribution

Computational Mathematics and Modeling 2019年第3期30卷 302-310页

作者： Kozlov, V.D. Maysuradze, A.I. Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University Moscow Russian Federation

Point estimation methods for the three-parameter lognormal distribution are investigated and compared. The lognormal distribution is required in many topical areas, but so far there have been no comparative studies of the various estimation methods. We show that despite the large number of traditional estimation methods, the lognormal distribution requires special methods. We accordingly consider specializations of the main parameter estimation approaches, including the actively developing distance minimization methods. Their accuracy and speed are compared on simulated data. We show that specialized parameterestimation methods may outperform the highly popular maximum likelihood method. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

关键词： distance minimization methods maximum likelihood method moment methods point estimation problem-oriented methods three-parameter lognormal distribution

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Separation of a Mixture of Three-Parameter Lognormal Distributions in the Analysis of Communication Environments

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Computational Mathematics and Modeling 2019年第3期30卷 311-319页

作者： Kozlov, V.D. Maysuradze, A.I. Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University Moscow Russian Federation

methods for the separation of a mixture of three-parameter lognormal distributions are investigated theoretically and empirically in the context of modeling message transmission delays in a computer cluster communication environment. Delay modeling based on mixtures of three-parameter lognormal distributions is proposed and parameter estimation methods for such models are investigated. Identifiability of the given family of distributions is proved, which is a necessary condition for the mixture separation problem to be well-posed. The proposed problem-oriented modifications of the standard algorithms are shown to be superior to the traditional methods. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

关键词： computer cluster communication environment EM-algorithm identifiability of a family of distributions message transmission delays point estimation problem-oriented methods separation of a mixture of distributions three-parameter lognormal distribution

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