The distribution of seismic moment is of capital interest to evaluate earthquake hazard, in particular regarding the most extreme events. We make use of likelihood-ratio tests to compare the simple Gutenberg-Richter power-law distribution with two statistical models that incorporate an exponential tail: the so-called tapered Gutenberg-Richter and the truncated gamma, when fitted to the global CMT earthquake catalog. The outcome is that the truncated gamma model outperforms the other two models. If simulated samples of the truncated gamma are reshuffled in order to mimic the time occurrence of the order statistics of the empirical data, this model turns out to be able to explain the empirical data both before and after the great Sumatra-Andaman earthquake of 2004.