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<p>The presence of asymmetry in geotechnical data necessitates the use of advanced techniques to handle skewness and kurtosis. A considerable amount of statistical literature has been developed over the years for such scenarios. Techniques ranging from transformations to heavy-tailed distributions, these tools and frameworks have been adapted to model a variety of geotechnical phenomena. At its essence, soil data is heterogeneous while also being asymmetric, posing challenges from a modelling perspective. Adopting an unsupervised learning paradigm, mixture model-based approach has shown great efficacy for modelling such scenarios. In particular, the use of transformations within a model-based framework has proven to be effective in dealing with skewed data. Despite the popularity of transformation techniques, there is a general paucity within the literature regarding the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(S_\text {U}\)</EquationSource> </InlineEquation> Johnson distribution. An alternative to the popularized power transformation, the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(S_\text {U}\)</EquationSource> </InlineEquation> Johnson distribution has been shown within geotechnical applications to have superior performance overall. In this work, we develop a mixture model-based approach for modelling incomplete and asymmetric soil data using finite mixtures of multivariate <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(S_\text {U}\)</EquationSource> </InlineEquation> distributions. Additionally, we also develop an imputation method to handle missing data scenarios. Using Shanghai soil data, our method proves itself highly robust in the presence of heterogeneity, and asymmetry.</p>

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Modelling Shanghai soil properties with finite mixtures of \(S_\text {U}\) Johnson distributions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月11日

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  • Nikola Počuča,
  • Michael P. B. Gallaugher,
  • Paul D. McNicholas

摘要

The presence of asymmetry in geotechnical data necessitates the use of advanced techniques to handle skewness and kurtosis. A considerable amount of statistical literature has been developed over the years for such scenarios. Techniques ranging from transformations to heavy-tailed distributions, these tools and frameworks have been adapted to model a variety of geotechnical phenomena. At its essence, soil data is heterogeneous while also being asymmetric, posing challenges from a modelling perspective. Adopting an unsupervised learning paradigm, mixture model-based approach has shown great efficacy for modelling such scenarios. In particular, the use of transformations within a model-based framework has proven to be effective in dealing with skewed data. Despite the popularity of transformation techniques, there is a general paucity within the literature regarding the \(S_\text {U}\) Johnson distribution. An alternative to the popularized power transformation, the \(S_\text {U}\) Johnson distribution has been shown within geotechnical applications to have superior performance overall. In this work, we develop a mixture model-based approach for modelling incomplete and asymmetric soil data using finite mixtures of multivariate \(S_\text {U}\) distributions. Additionally, we also develop an imputation method to handle missing data scenarios. Using Shanghai soil data, our method proves itself highly robust in the presence of heterogeneity, and asymmetry.