We point out that the functional form describing the frequency of sizes of events in complex
systems (e.g. earthquakes, forest fires, bursts of neuronal activity) can be obtained from maximal
likelihood inference, which, remarkably, only involve a few available observed measures such as
number of events, total event size and extremes. Most importantly, the method is able to predict
with high accuracy the frequency of the rare extreme events. To be able to predict the few, often
big impact events, from the frequent small events is of course of great general importance. For a
data set of wind speed we are able to predict the frequency of gales with good precision. We analyse
several examples ranging from the shortest length of a recruit to the number of Chinese characters
which occur only once in a text.