1 research outputs found
Extremal Indices in the Series Scheme and their Applications
We generalize the concept of extremal index of a stationary random sequence
to the series scheme of identically distributed random variables with random
series sizes tending to infinity in probability. We introduce new extremal
indices through two definitions generalizing the basic properties of the
classical extremal index. We prove some useful properties of the new extremal
indices. We show how the behavior of aggregate activity maxima on random graphs
(in information network models) and the behavior of maxima of random particle
scores in branching processes (in biological population models) can be
described in terms of the new extremal indices. We also obtain new results on
models with copulas and threshold models. We show that the new indices can take
different values for the same system, as well as values greater than one