  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.
