Fitness of seven distribution functions to annual maximum data of rainfall depth is compared. The distributions include six conventionally used ones and SQRT-ET-max distribution derived by the authors as a distribution function of annual maxima of total depth of a single rainfall. A proceeure to evaluate the fitness, especially in the region of excessively large rainfall, is proposed in view of a theoretical distribution function of average recurrence interval of historical maximum records and the Kolmogorov-Smirnov test. It is applied to annual maximum data of 10-minute to 6-hour rainfall depths observed at observatories in Hokkaido and of daily rainfall throughout Japan.