Validation of appropriate estimation criteria for the number of components for separating a polymodal grain-size distribution into lognormal distributions

Abstract

Polymodal particle size distributions are generally analyzed by separating them into lognormal distributions, but estimating the precise number of lognormal components required remains a considerable problem. In the present study, appropriate evaluation criteria for the estimation of the number of components were examined by using artificial data for which the true number of components was known. The characteristics of estimations of the number of components by four evaluation criteria, the mean square error (MSE), Akaike information criterion (AIC), Bayesian information criterion (BIC), and adjusted R-squared (ARS), were investigated. The results showed that the MSE and ARS were less sensitive to the true number of components and tended to overestimate the number of components. By contrast, the AIC and BIC tended to underestimate the number of components, and their correct answer rates decreased as the true number of components increased. The BIC tended to include the true number of components among its higher ranked models. The present evaluation results suggest that the MSE, although frequently used, is not necessarily the most appropriate evaluation criterion, and that the AIC and ARS may be more appropriate criteria. Furthermore, checking whether the number of components estimated by the AIC or ARS is included among higher ranked BIC models might prevent overestimation and thereby allow for more valid estimation of the number of components. When the criteria were applied to grain-size distributions of lacustrine sediments, it was possible to estimate the number of components that reflected differences in grain-size distribution characteristics.