The authors have presented a probability density function of total rainfall depth of a single storm. It is expressed in terms of the second kind modified Bessel's function. Using the asymptotic expansion of the function, a simple probability density function of the annual maximum precipitation depth is derived. which is named “SQRT-exponentialtype distribution of maximum” The p. d. f. is long-tailed compared with the Gumbel's distribution, which suggests higher probability of the occurrence of record-breaking large precipitations or so-called outliers. For example, the historical maximum 24-hour precipitation at Osaka (283.7mm) is reasonably evaluated by means of the p. d. f. as once a 214-year precipitation, while Gumbel's distribution evaluates it as once a 955-year precipitation, which is apparently unrealistic.