This paper presents an original methodology to estimate delay risk a few days before operations with generalized linear models. These models represent a given variable with any distribution from the exponential family, allowing to compute for any subject its own probability distribution according to its features. This methodology is applied on small delays (less than 20 minutes) of high-speed trains arriving at a major french station. Several distributions are tested to fit delay data and three scenarios are evaluated: a single GLM with a negative binomial distribution and two two-part models using both a logistic regression as first part to compute the probability of arriving on time, and a second part using a negative binomial or a lognormal distribution to obtain the probabilities associated with positive delay values. This paper also proposes a validation methodology to assess the quality of these probabilistic predictions based on two aspects: calibration and discrimination.