If subduction zone earthquakes conform to a characteristic model, in which persistent segments fail at predictable stress levels due to the steady accumulation of tectonic loading, historical seismicity may constrain the occurrence of future events. We test this model for earthquakes on the Sumatra-Andaman megathrust and other subduction zones using frequency-magnitude distributions. Using simulations, we show that Poisson confidence intervals correctly account for the counting errors of histogram data. These confidence intervals demonstrate that we cannot reject the Gutenberg-Richter distribution in favor of a characteristic model in any of the real catalogues tested. A visual bias in power-law count data at high magnitudes, combined with a sample bias for large earthquakes, is sufficient to explain candidate characteristic events. This result implies that historical earthquakes are likely poor models for future events and that Monte Carlo simulations will provide a better assessment of earthquake and associated hazards.