Although the two-parameter Beta distribution is the standard distribution for

analyzing data in the unit interval, there are in the literature some useful and interesting alternatives which are often under-used. An example is the two parameter complementary Beta distribution, introduced by Jones (2002) and, to the best of our knowledge, used only by Iacobellis (2008) as a probabilistic model for the estimation of T year flow duration curves. In his paper the parameters of complementary Beta distribution were successfully estimated, perhaps due to its simplicity, by means of the L-moments method. The objective of this paper is to compare, using Monte Carlo simulations, the bias and mean-squared error, of the estimators obtained by the methods of L-moments and maximum likelihood. The simulation study showed that the maximum likelihood method has bias and mean -squared error lower than L-moments. It is also revealed that the parameters estimated by the maximum likelihood are negatively biased, while by the L-moments method the parameters are positively biased. Data on relative indices from annual temperature extremes (percentage of cool nights, percentage of warm nights, percentage of cool days and percentage of warm days) in Uruguay are used for illustrative purposes.