Doctoral School Mathematics and Scientific Computing

Abstract: he motivation for this work originates in an application of generalized linear models to a problem from the paper and printing industries. The aim is to unravel dependencies between the successful transfer of the printing ink and certain properties of the paper (e.g. topography) in order to gain a better knowledge of the underlying processes. Of the resulting logistic regression models, some display overdispersion whereas others feature underdispersion.

Which is why this work tries to employ two distributions that can account for the additional or lesser variability of the data compared to the classic binomial distribution. Both distributions originate from the classic binomial distribution but carry an additional parameter that enables the distribution to react to variabilities smaller or larger than in the binomial case.

An overview of these distributions will be given, followed by an embedding into the framework of generalized linear models. Simulation results will show the performance of the parameter estimation via maximum likelihood estimation. Finally, the presentation will conclude with a comparison of the three models resulting from the different distributions, applied to the dataset of successful or failed ink transfer. [hide abstract]