What sort of analysis you want to do? You may use frequency analysis, i.e. Gumbel, Weibull etc. You may analyze the maximum and minimum rainfall frequencies (extreme events). Please refer to Engineering Hydrology by K. Subramania, Watershed Hydrology by R. Suresh). Even you may use Standard Precipitation Index for this purpose. You may find all the source codes in the web that could be used in Math-Lab.
This would depend on what the aims of the research would be, and the type of data available (e.g. monthly, weekly, daily or 15-minute precipitation totals). For example, some are interested in simple analyses of changing rainfall amounts over time. However, many researchers (climatologists, hydrologists and water resource specialists) and environmental managers are looking at shifting patterns of rainfall intensities or the frequency of heavy daily rainfalls above given thresholds, e.g. 20mm, 25mm 50mm, 75mm: these are usually important for flood risk.
A further key interest is in changing rainfall seasonality over time. You may want to check out our early paper on this which developed and applied a simple Rainfall Seasonality index to UK and tropical environments. This is quite simple to apply, but quite well used, and can be based on monthly data too.
Reference is (Abstract on Research Gate):
Weather, vol 36, pp. 201-208, RAINFALL SEASONALITY: DESCRIPTION, SPATIAL PATTERNS AND CHANGE THROUGH TIME, by R. P. D. Walsh and D. M. Lawler
If you have mapped your rainfall data, you can use geostatistical analysis toobar in Arcgis, it's wizard helps to analyze data for different statistical methods such as kriging and interpolations.