This paper improves upon an existing extreme precipitation monitoring system based on the Tropical Rainfall Measuring Mission (TRMM) daily product (3B42) using new statistical models. The proposed system utilizes a regional modeling approach, where data from similar locations are pooled to increase the quality of the resulting model parameter estimates to compensate for the short data record. The regional analysis is divided into two stages. First, the region defined by the TRMM measurements is partitioned into approximately 28,000 non-overlapping clusters using a recursive k-means clustering scheme. Next, a statistical model is used to characterize the extreme precipitation events occurring in each cluster. Instead of applying the block-maxima approach used in the existing system, where the Generalized Extreme Value probability distribution is fit to the annual precipitation maxima at each site separately, the present work adopts the peak-over-threshold method of classifying points as extreme if they exceed a pre-specified threshold. Theoretical considerations motivate using the Point Process framework for modeling extremes. The fitted parameters are used to estimate trends and to construct simple and intuitive average recurrence interval (ARI) maps which reveal how rare a particular precipitation event is. This information could be used by policy makers for disaster monitoring and prevention. The new methodology eliminates much of the noise that was produced by the existing models due to a short data record, producing more reasonable ARI maps when compared with NOAA's long-term Climate Prediction Center ground-based observations. Furthermore, the proposed methodology can be applied to other extreme climate records.