  We introduce two classes of multivariate log skewed distributions with normal
kernel: the log canonical fundamental skew-normal (log-CFUSN) and the log
unified skew-normal (log-SUN). We also discuss some properties of the log-CFUSN
family of distributions. These new classes of log-skewed distributions include
the log-normal and multivariate log-skew normal families as particular cases.
We discuss some issues related to Bayesian inference in the log-CFUSN family of
distributions, mainly we focus on how to model the prior uncertainty about the
skewing parameter. Based on the stochastic representation of the log-CFUSN
family, we propose a data augmentation strategy for sampling from the posterior
distributions. This proposed family is used to analyze the US national monthly
precipitation data. We conclude that a high dimensional skewing function lead
to a better model fit.
