SUMMARY
This paper identifies various statistical problems in the measurement and analysis of particle sizes. The log‐skew‐Laplace distribution is proposed as a simple but effective model for particle sizes which can be readily extended to handle more complex situations such as mixtures and the marrying of measurements of different aspects of size. The model is compared with other contenders, the log‐normal and log‐hyperbolic distributions, in the analysis of sand grain data from the Hebrides.
Summary
This paper describes the statistical analysis and modelling of simple and ‘mixed’ particle mass-size distributions. The particular sediments discussed derive from modern climbing, seif and barchan dunes. The statistical methods considered include calculation of sample moments (mean, sorting, skewness and kurtosis), in particular by semigraphical techniques. Additionally, attention is given to the construction of log normal probability plots and their supposed interpretation in terms of distinct segments representing different components of a ‘mixed’ distribution. Whilst these techniques have been used with some effect in the case of analysing simple or pure sand samples, it is shown that their application to mixed size distributions can be misleading. The approach advocated as an alternative is to model the size distribution directly by one of a family of parametric statistical distributions and use the estimated parameters to characterize the individual samples. The particular family preferred is the three-parameter log skew Laplace, which can be extended readily to a seven-parameter family incorporating mixture densities. This family provides computational advantages over the log hyperbolic family, whilst retaining its geological interpretability and theoretical derivation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.