  Severe Ionosphere magnetic storms are feared events for integrity and
continuity of navigation systems such as EGNOS, the European SBAS
(Satellite-Based Augmentation System) complementing GPS and an accurate
modelling of this event probability is necessary. Our aim for the work
presented in this paper is to give an estimation of the frequency of such
extreme magnetic storms per time unit (year) throughout a solar cycle. Thus, we
develop an innovative approach based on a proportional hazard model, inspired
by the Cox model, with time dependent covariates. The number of storms during a
cycle is supposed to be a non-homogeneous Poisson process. The intensity of
this process could be expressed as the product of a baseline risk and a risk
factor. Contrary to what is done in the Cox model, the baseline risk is one
parameter of interest (and not a nuisance one), it is the intensity to
estimate. As in Extreme Value Theory, all the high level events will be used to
make estimation and the results will be extrapolated to the extreme level ones.
After a precise description of the model, we present the estimation results and
a model extension. A prediction for the current solar cycle (24th) is also
proposed.
