Comments on Schoenberg et al. (2003)

This article comments on the work of Schoenberg FP et al., “On the distribution of wildfire sizes. Environmetrics. 2003;14:e605. https://doi.org/10.1002/env.605.” These comments are mainly about both numerical and visual goodness‐of‐fit criteria, used for comparing the performance of candidate distributions for wildfire sizes. First, the maximum likelihood estimate of the half‐normal distribution and its corresponding goodness‐of‐fit criterions are corrected. Then, the given values of the Akaike information criterion for all fitted models are modified. Furthermore, some comments on the inappropriateness of naming the proposed statistic under the “Cramér–von Mises (C‐vM) statistic” are given. After presenting the C‐vM statistic, its values and the corresponding p values, which show the goodness‐of‐fit–proposed distributions for describing the data, are calculated. At the end, the asymptotic confidence bounds for the “fitted comparison line” in quantile–quantile plots of two best‐fitted distributions are given. Comparing these asymptotic bounds with their counterparts in Schoenberg et al., named “Confidence bounds based on Monte Carlo simulation,” bear great similarity in the position of the end points, while creating them cost relatively much cheaper computations.