Statistics and Its Interface

Volume 8 (2015)

Number 1

Special Issue on Extreme Theory and Application (Part II)

Guest Editors: Yazhen Wang and Zhengjun Zhang

A proportional hazard model for storm occurrence risk

Pages: 71 – 84



Malika Chassan (Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse, France; and CNES, Toulouse, France)

Jean-Marc Azais (Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse, France)

Guillaume Buscarlet (Thales Alenia Space, Toulouse, France)

Norbert Suard (CNES, Toulouse, France)


The aim of this paper is to give a precise estimation of the extreme magnetic storms frequency per time unit (year) throughout a solar cycle. An innovative approach based on a proportional hazard model is developed. Based on the Cox model, this method includes non-stationarity and covariate influence. The model assumes that the number of storms during a cycle is a non-homogeneous Poisson process. The intensity of this process can be expressed as the product of a baseline risk and a risk factor. In the Cox model, the baseline risk is a nuisance parameter. In our model, it is a parameter of interest that will be estimated. The risk factor depends on a covariate, the solar activity index. As in Extreme Value Theory (EVT) and especially in Peaks Over Threshold (POT) modeling, all the high level events are used to make estimations and the results are extrapolated to the extreme level events. This study highlights a strong correlation between the occurrence intensity of magnetic storms and their position on the solar cycle. The model can be used to forecast occurrence intensity for the current 24th solar cycle.

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