This article explores how to interpret observations of rates of seismic- moment release by evaluating simulated earthquake sequences generated assuming Gutenberg–Richter (gr), truncated gr, or exponentially tapered gr distributions. For earthquakes generated assuming a gr distribution, expected moment rates depend strongly on the largest event observed and increase indefinitely over time, never approaching a stable value. For events generated with truncated or tapered distributions expected moment rates increase with time but approach a stable value if moments near the corner moment MC are thoroughly sampled. Thus, interpreting reported moment rates requires knowledge of the corner moment MC and the number N of contributing earthquake observations. This article discusses how to estimate a critical number of events Nlarge where the approach to stability begins; Nlarge depends more strongly MC than on the β-value, and only weakly on whether one simulates the observations with a truncated or tapered gr distribution. For situations where N is less than Nlarge, the article discusses how to adjust moment rates to account for the expected time dependence and also explores ways for estimating rates that reduce the dependence on the largest event.