Bayesian Robustness Modelling Using the Floor Distribution

Abstract

In Bayesian analysis, the prior distribution and the likelihood can conflict, in the sense that they can carry diverse information about the parameter of interest. The most common form of conflict is the presence of outliers in the data. Usually, problems of conflicts are solved by assigning heavy-tailed distributions to that source of information which may be causing the conflict. However, the class of heavy-tailed distributions is not well defined, therefore there are many ways to define heavy tails. The class O-regularly varying distributions is rather unknown in Statistics, it basically embraces those distributions whose tails decay oscillating between two power functions. In this work we study a new distribution which has this property and, as a consequence, yields robust models for location and for scale parameter models separately. We provide explicit expressions for some relevant quantities concerning the distribution, such as the moments, distribution function, etc. Besides, we show how conflicts can be resolved using this distribution.