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Due to climate change, extreme rainfall and drought events are becoming more and more frequent in several regions of the globe. We investigated the suitability of employing statistical and fractal (or scaling) methods to characterise extreme precipitation and drought events. The case of the island of Mauritius was considered, for which monthly mean rainfall data for the period January 1950 to December 2016 were analysed. The generalised extreme value distribution was used to extract the 10- and 20-year return levels and the Standardised Precipitation Index (SPI) was used to identify anomalous wet and dry events. A log-term correlation analysis was also performed to characterise the relationship between maximum rainfall and its duration. The results indicate that the 10-year return level is approximately between 500 mm and 850 mm and the 20-year return level is between 600 mm and 1000 mm. Results also show that the extreme maximum rainfall events occur mostly during austral summer (November to April) and could be related to the effects of tropical cyclones and La Niña events, while anomalous dry events were found to be significantly persistent with very long periods of drought. Moreover, there was a strong correlation between maximum rainfall and its duration. The methodology used in this work could be very useful in similar studies for other Small Island Developing States.