Some Investigations into the Class of Exponential Power Distributions

In this thesis, methods are developed relating to the exponential power class of distributions. Paper I considers Bayesian linear mixed models where the usual normality assumption is replaced by the multivariate exponential power distribution. Particular focus lies on Bayesian testing of the fixed effects. Paper II introduces a score test for the shape parameter of the exponential power distribution. A Pitman-type local analysis is used to establish asymptotic results. Paper III investigates quantile regression based on the skewed exponential power distribution. The bridge between standard and Lp quantiles is of particular interest. Paper IV investigates Bayesian composite Lp-quantile regression based on the skewed exponential power distribution. Paper V considers Bayesian composite quantile regression with a particular interest in es-tablishing theoretical justification from a non-parametric Bayesian perspective