The statistical analysis of ‘mixed’ grain size distributions from aeolian sands in the Libyan Pre-Desert using log skew Laplace models

Abstract

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.

Statistical Characterization of Grain-Size Distributions in Sandy Fluvial Systems

“…Barndorff-Nielsen et al (1982) used the log-hyperbolic distribution to examine variation in grain size in a sequence of sand samples along an eolian dune, as did Sutherland and Lee (1994) in their characterization of Hawaiian beach sands. The log-skew-Laplace distribution was found to be the best model for littoral sands from the Hebrides (Fieller et al 1992) and Libyan eolian sediments (Flenley et al 1987).…”

“…For example, some authors have proposed that fluvial grain-size distributions can be sufficiently approximated by a lognormal distribution (e.g., Kothyari 1995;Kranck et al 1996aKranck et al , 1996bPurkait 2002). In contrast, other work has shown that other distributions, including log-skew-Laplace and log-hyperbolic distributions, fit some sediment samples better than log-normal distributions (e.g., Barndorff-Nielsen et al 1982;Fieller et al 1984;Flenley et al 1987;Fieller et al 1991;Fieller et al 1992). While some have proposed explanations for why certain parametric distributions fit better than others (e.g., , the underlying causes are unknown, in part because of a lack of quantitative studies on the subject, and differences in strategies for sediment sampling, measuring, and statistical analysis.…”

Statistics of Particle Size Data

“…The obvious approach is to model the size distribution by a mixture distribution. Flenley (1985) and Flenley et al (1987) describe the use of a (seven-parameter) mixture of two log-skew-Laplace distributions to analyse such data.…”

Factors affecting the distribution of commercially exploited penaeid prawns (shrimp) (Decapod:Penaeidae) across the northern Great Barrier Reef, Australia

“…Therefore the comparison of the coefficients and μ give a simple but effective way to compare complex particle size distributions. SHEFSIZE (University of Sheffield, UK) was used for fitting these summary statistical models to the particle size data (Fieller et al, 1984;Flenley et al, 1987: N. Fieller, University of Sheffield, personal communication).…”