Two recently developed point process models for temporal rainfall are tested using 7 years of hourly rain gauge data obtained from Majuro and Truk atolls in the northern equatorial Pacific. The models were fit to data from two seasons, winter (January--March) and summer (June--August). The results indicate that neither model can adequately reproduce the observed statistics for both seasons. A new model is proosed which characterizes the random nature of small convective events and the event like occurrences of large tropical convective cloud clusters. The model is shown to be superior to the previous models in reproducing the first- and second-order moments of tropical rainfall as well as occurrence statistics such as the probability of rainfall and the expected rainfall conditional on rain. ¿ American Geophysical Union 1993