ruth@utstat.UUCP (10/04/87)
TOPIC: MODEL CHOICE AND EXTREMES
SPEAKER: Martin A.J. van Moutfort
Dept. of Mathematics, Wageningen Agricultural Univ.
DATE: October 9, 1987, 1:00 P.M.
PLACE: Sidney Smith Hall, Room 1086
ABSTRACT:
Safety is connected with probabilities on extreme events (e.g. dyke
height and maximal height of the sea level).
Theory supports a Generalized Extrema Value (GEV) distribution for
extremes with a location (mu), scale (sigma) and shape (theta)
parameter, where the shape parameter heavily influences the tail
behavior. The well known and frequently used Gumbel distribution is a
special case of GEV: theta = 0.
Inference on the distribution of extremes can be based on extremes, or
on the number and sizes of exceedances over a threshold (POT: peaks over
threshold). Modelling POT-data by a Poisson number of exceedances with
Exponentially distributed sizes gives rise to a Gumbel distribution for
the maximum; replacing the Exponential distribution by the Generalized
Pareto distribution (GPD) results in a GEV for the maximum.
Evidence for GEV can be based on extremes or on POT-data. The
performance of some quick tests for GEV versus Gumbel and for GPD versus
Exponential is discussed. Attention is also paid to the problem of lack
of fit in the one tail when the attention has to be focussed on the
other tail.