Insurance risks data typically exhibit skewed behaviour. In this paper, we propose a Bayesian approach to capture the main features of these data sets. This work extends a methodology recently introduced in the literature by considering an extra parameter that captures the skewness of the data. In particular, a skewed Student‐t distribution is considered. Two data sets are analysed: the Danish fire losses and the US indemnity loss. The analysis is carried with an objective Bayesian approach. For the discrete parameter representing the number of the degrees of freedom, we adopt a novel prior recently appeared in the literature. Copyright © 2017 John Wiley & Sons, Ltd.