The statistical distribution of 1-day (one reading in 24 hours) and 24-hour (several readings in 24 hours) annual maxima is considered and a transformed extreme value type 1 distribution function (TDF) that includes a probable maximum (PM) value is suggested. The distribution function fits standardized annual maximum station values from Iceland and Washington State very well. A generalized distribution function, derived from the TDF, is suggested. To use it, two local parameters have to be known; the 5-year event, M5, that must be picked from a map and a slope factor, Ci, that is a function of the coefficient of variation. The variation of Ci between independent observation stations is assumed to be random, and guidelines on how a Ci may be selected are discussed. The generalized distribution function is used to calculate quantile estimates and a local probable maximum precipitation (PMP). Regional PMPs can be calculated by maximizing this value. Two independent sets of Ci's compare favorably: (1) a statistical set compiled from the British Natural Environment Resource Council (NERC) PMP envelope and (2) a meteorological set calculated from U.S. National Weather Service estimates of PMP for Washington State. The regional PMP estimates calculated from the generalized distribution also compare favorably with the NERC PMPs, except that the estimates for low M5 produce up to 33% lower PMPs. This difference may be explained by a number of factors that are also discussed.¿ 1997 American Geophysical Union