Résumé
Following the financial literature on risk management, this paper introduces some risk measure for train delay time in the probabilistic framework. The measures of extreme risk are defined as quantile of train delay time assumed as positive continuous random variables. Their close-formed expressions and empirical calibration are discussed under the assumptions of log-normal, log-t-Student and Weibull distributions. A method for the performance evaluation of the proposed measure is presented. Finally, an empirical study illustrates the effectiveness of our modeling approach and shows the interest of its practical application.