Modelling Shanghai soil properties with finite mixtures of SU Johnson distributions

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 SU Johnson distribution. An alternative to the popularized power transformation, the SU 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 SU 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.