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.

多峰粒度分布通常通过将其分成对数正态分布来进行分析，但估计所需对数正态分量的精确数量仍然是一个相当大的问题。在本研究中，通过使用已知成分真实数量的人工数据来检查用于估计成分数量的适当评估标准。研究了均方误差（MSE）、赤池信息准则（AIC）、贝叶斯信息准则（BIC）和调整R平方（ARS）四种评价标准估计成分数量的特性。结果表明，MSE和ARS对真实成分数量不太敏感，并且倾向于高估成分数量。相比之下，AIC 和 BIC 往往会低估组件的数量，并且它们的正确答案率随着真实组件数量的增加而下降。 BIC 倾向于在其排名较高的模型中包含真实的组件数量。目前的评价结果​​表明，MSE虽然经常使用，但不一定是最合适的评价标准，AIC和ARS可能是更合适的标准。此外，检查 AIC 或 ARS 估计的组件数量是否包含在排名较高的 BIC 模型中可能会防止高估，从而可以更有效地估计组件数量。当该标准应用于湖相沉积物的粒度分布时，可以估计反映粒度分布特征差异的成分数量。