If risk-based criteria are used in the design of high hazard structures (such as dam spillways and nuclear power stations), then it is necessary to estimate the annual exceedance probability (AEP) of extreme rainfalls up to and including the Probable Maximum Precipitation (PMP). This paper describes the development and application of two largely independent methods to estimate the frequencies of such extreme rainfalls. One method is based on stochastic storm transposition (SST), which combines the “arrival” and “transposition” probabilities of an extreme storm using the total probability theorem. The second method, based on “stochastic storm regression” (SSR), combines frequency curves of point rainfalls with regression estimates of local and transposed areal rainfalls; rainfall maxima are generated by stochastically sampling the independent variates, where the required exceedance probabilities are obtained using the total probability theorem. The methods are applied to two large catchments (with areas of 3550 km² and 15,280 km²) located in inland southern Australia. Both methods were found to provide similar estimates of the frequency of extreme areal rainfalls for the two study catchments. The best estimates of the AEP of the PMP for the smaller and larger of the catchments were found to be 10⁻⁷ and 10⁻⁶, respectively, but the uncertainty of these estimates spans one to two orders of magnitude. Additionally, the SST method was applied to a range of locations within a meteorologically homogenous region to investigate the nature of the relationship between the AEP of PMP and catchment area.