| An examination is made of the true return periods associated with certain types
of composite indices for the rareness of events. In particular, return periods are
evaluated separately for several different ways of describing how bad an event was, and
the composite index, or apparent return period, is defined as the largest of these
component return periods. Such apparent return periods give an incorrect indication of
how often a larger value for the composite index will occur. Simulations are used to
study the relationship between the true and apparent return periods for some simple cases,
and an assessment is made of the extent of the error made if the apparent return period is
used directly. A simple practical procedure is described for dealing with real datasets
without model-fitting, and this is assessed using further simulations. An example is given
relating to a possible flood situation where a composite index is constructed as the
largest of the return periods of high rainfall-accumulations over a number of durations.
Keywords: drought severity index, composite index, event severity, return period |