Extreme rainfall events can pose a major risk for flooding in many locations on the Hawaiian Islands. There is a general interest in understanding how future extreme rain events may become more or less intense. We took a look at the daily rainfall events in Hawaii during the years 1990 to 2014 and compared how well a one of the standard mathematical functions describes the rainfall intensities. We used statistical methods to estimate the Gamma-distribution function that best reproduces the observed data. This was done for selected locations on the islands in order to cover a wide range of different local climates. Then we compared rainfall intensities from the mathematical model with the behavior of extreme rainfall events in actual rainfall data. The statistical analysis showed that differences in the wet and dry season rainfall are captured by the Gamma function model, but there is still an underestimation of the number of occurrences with extreme rainfall intensities. We applied the Gamma distribution function also to study how effective it is in the assessment of changes in extreme events. The results tell us that the alternatives to the Gamma function should be used for accurate representation extreme rainfall statistics in Hawaii.