An outlier is a very large or very small value that does not follow the general trend of a given data set. Outliers in rainfall data cause uncertainty in water engineering studies and estimated design events. As such, an additional mathematical tool for dealing with outliers is needed. One of the main issues in hydrologic frequency analysis is the problem of mixed distributions or multiple populations in hydrologic time series. Univariate probability distributions are unsuitable for data sets with outliers, therefore three mixed distributions (mixed Gumbel, mixed GEV, EV1–GEV) were used in this paper. The mixed Gumbel distribution was found to be the best distribution to fit to the 24-h annual maximum rainfall data at all of the rainfall gauging stations used in this study, on the basis of the minimum standard error of fit.