How do I start and go about analyzing the variability of extreme rainfalls in a region? I have a gridded dataset of monthly precipitation and would like to analyze the variability of extreme rainfall. However, aside from looking at the overview of basic statistics (mean, standard deviation, max and min amount of rainfall), I don't really know how to start seeing the picture of the variability of extremes in my analysis. Any advice or recommendation on relevant readings is appreciated!

If you just have one-dimensional data, you could do a box plot thereof, and everything beyond the whiskers is considered outliers.
If you want to presume approximate normality, you can take the z-score as an anomaly score and decide about a threshold yourself.
If you have time series data, you might want to look into belonging libraries like e.g. the R package tsoutliers.
If you also want to do spatial comparisons, i.e. compare precipitation of different locations and want to find outliers, i.e. rare values for precipitation, I would recommend isolation forest.
