Parametric and non-parametric evaluation of conversion of number-based particle size distribution to mass-based distribution

Interest in applying non-parametric methods to analyze particle size distribution (PSD) is growing. Previous studies have demonstrated the effectiveness of the bootstrap method in evaluating percentile values and confidence intervals for number-based PSD data. In this study, the application of the method to mass-based (volume-based) distribution was extended. The performance of the parametric method, which uses the Hatch-Choate equation for lognormal distribution, was compared with that of the non-parametric method in evaluating mass-based distribution data converted from number-based distribution. The superior performance of the parametric method underscores the importance of prior distribution function knowledge. For non-parametric methods, “real repeat” simulations involving 5000 repetitions of individual samplings were conducted as a reference for the bootstrap method. It was found that there exists a critical sample size, beyond which larger samples are necessary to accurately represent the population through non-parametric analysis. This critical size requires that the maximum size in the dataset exceeds the target size (e.g., the 90th percentile value) for direct evaluation of existing data. When the sample size range surpasses the critical size, bootstrap provides a good approximation to the “real repeat” experiments. Therefore, it is essential to have a diagnostic strategy to determine whether the sample size is sufficiently large for non-parametric analysis. A simple method using multi-scale bootstrap is proposed in this regard.