The mean difference between the cumulative percent values of a grain-size distribution and the corresponding ideal Gauss distribution is a measure for goodness-of-fit. This is also true for other types of distributions that are applied in grain-size analysis, for example, the Rosin distribution. The corresponding ideal Gauss or Rosin distribution is calculated from the mode of the grain-size distribution and the gradient of the central part of its cumulative curve plotted on lognormal probability paper and Rosin paper, respectively. The degree of linearity of the cumulative curve on lognormal probability paper or Rosin paper is not, however, a measure of fit, because although grain-size distributions are always finite and truncated on both sides, the cumulative curves of the corresponding ideal Gauss and Rosin distributions are curved at the margins. Gauss and Rosin goodness-of-fit values are two additional grain-size parameters. In contrast to the classical grain-size parameters (mean, sorting, skewness, kurtosis, etc.), they characterize the functional relation between grain size and frequency. Because the Rosin distribution type seems to be a "source-rock-specific" feature and because lognormality is a hydraulically controlled, "transport-specific" feature based on sorting effects, the quantification of this functional relation may be used as a measure of textural maturity.

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