You need to divide the area of interest to grids similar to TRMM pixels. Then get archived data sets for daily or weekly rainfall for the region and generate your own monthly means. A few station data also can be collected on daily rainfall and avalidation of TRMM monthly means can be carried out to know the error bars. I did a similar exercise for aerosol data from MODIS satellite.
Doing the computation is fine of course, but how to judge the credibility of it is another issue. The spatiotemporal representation is an issue as local rain gauges have a different daily rain PDF than a PDF obtained from daily sums from a few TRMM passes. So, the rain rate PDF may be correct over a typical TRMM pixel, but not validate well with a local rain gauge, e.g., in areas with orography. The daily temporal error due to non-uniform TRMM sampling, as compared to the uniform sampling by a rain gauge will be substantial as well, e.g., daily afternoon rain could be missed by TRMM systematically. An attempt of error analysis is given in: Alemohammad et al., Hydrol. Earth Syst. Sci. Discuss., 12, 2527–2559, 2015