Delays in public transportation are a nuisance to many people and they cause huge cost to society. Any scientific alleviation of this problem will in general rely on high quality data, precise modelling and accurate analysis. Considering a transport system – for instance the public transport in the greater Copenhagen area – these delays are difficult to model for two reasons. Firstly, there are large interdependencies between the different services, as delays at one place will influence travel times of services in other parts of the network due to crowding and rerouted travelers. Secondly, the data is inherently skewed attaining only non-negative values and with possible atoms at zero corresponding to no delay. The result is thus data which is both multivariate and non-normally distributed.
Today multivariate data is usually analyzed using parametric methods, which rely on a normal assumption, or by using non-parametric and heuristic methods. The first approach is clearly not suited for transport data due to the non-normal nature of the data, and the second approach lacks properly defined statistical tests. In this project we will turn to the class of multivariate matrix exponential distributions in order to model the data properly. Matrix exponential distributions are a very flexible class of distributions, and we hope that they can bridge the gap between the parametric and non-parametric approaches, by being based less restrictive assumptions than the former, and providing more rigid models than the latter. Due to the flexibility of the matrix exponential distributions, it is also likely that the results obtained in this project can be used to model other types of data with some of the same characteristics.