Comment on 'Candidate distributions for climatological drought indices (SPI and SPEI)' by James H. Stagge et al.

In opposition to the originally proposed Log-logistic distribution, Stagge et al. (2015) recommended the use of the general extreme value (GEV) distribution to calculate the standardized precipitation evapotranspiration index (SPEI). This is not an irrelevant issue, as the use of different distribution functions may lead to different SPEI values, and thus can make them not compatible with those of other users. Stagge et al. (2015) based their recommendation on the results of goodness-of-fit tests applied to climate data in Europe. Here we provide evidence that these tests do not have enough power for discriminating between very similar distribution functions. Even more, their results are not robust and depend on the data used. Other criteria based on the adaptation to the tails of the distribution and the fraction of cases with no solution are more relevant to guide the selection of the most adequate distribution. We have tested both distribution functions based on these criteria and using global gridded data of precipitation and reference evapotranspiration. Our results clearly recommend the use of the Log-logistic distribution to calculate the SPEI, as originally proposed by Vicente-Serrano et al. (2010a).