Single-sample unmixing and parametric end-member modelling of grain-size distributions with transformed probability density functions and their performance comparison using aeolian sediments

Parametric decomposition techniques including single-sample unmixing and parametric end-member model-ling are routine mathematical methods used for interpreting grain-size distributions. In this study, transformed probability density functions for the Lognormal, Weibull, Skew Normal, and Skewed Generalized Normal distri-butions are derived and efficient open-source numerical programs applying these functions are presented. These new functions contain two free shape parameters characterizing the peak position and magnitude of a unimodal distribution, and they can be more easily initialized and constrained compared to their original counterparts, as the two shape parameters can be estimated directly from the grain-size distribution or its derivatives and can only vary within very narrow intervals. This enables the decomposition to converge to both reproducible/stable and structurally/genetically reasonable solutions. The transformed functions are applied to grain-size distribu-tions of aeolian sediments collected from around the Tengger Desert, using both the single-sample unmixing and parametric end-member modelling methods, and the results of different functions are compared. The implications of the results for parametric decomposition of sediment grain-size distributions using unimodal mathematical distributions are discussed.(c) 2023 Elsevier B.V. All rights reserved.