Comparison of six particle size distribution models on the goodness-of-fit to particulate matter sampled from animal buildings

Lognormal distribution is often used as a default model for regression analysis of particle size distribution (PSD) data; however, its goodness-of-fit to particle matter (PM) sampled from animal buildings and its comparison to other PSD models have not been well examined. This study aimed to evaluate and to compare the goodness-of-fit of six PSD models to total suspended particulate matter (TSP) samples collected from 15 animal buildings. Four particle size analyzers were used for PSD measurement. The models' goodness-of-fit was evaluated based on adjusted R², Akaike's information criterion (AIC), and mean squared error (MSE) values. Results showed that the models' approximation of measured PSDs differed with particle size analyzer. The lognormal distribution model offered overall good approximations to measured PSD data, but was inferior to the gamma and Weibull distribution models when applied to PSD data derived from the Horiba and Malvern analyzers. Single-variable models including the exponential, Khrgian-Mazin, and Chen's empirical models provided relatively poor approximations and, thus, were not recommended for future investigations. A further examination on model-predicted PSD parameters revealed that even the best-fit model of the six could significantly misestimate mean diameter, median diameter, and variance. However, compared with other models, the best-fit model still offered the relatively best estimates of mean and median diameters, whereas the best predicted variances were given by the gamma distribution model. Particulate matter from animal buildings contains a large portion of coarse particles and, thus, has different particle size distribution (PSD) than ambient aerosols. The findings suggest a default use of the prevalent lognormal distribution model can lead to significant misestimates of PSD parameters such as mean diameter, median diameter, and variance. Other models, such as the gamma and Weibull distribution models, may be considered as alternative options. Because of a complexity in the shape of measured PSD profiles, the goodness-of-fit for each of the different PSD models must be compared before selecting one for data regression, parameter estimation, and reporting.