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

Abstract 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.