  Much work has been done in the area of the cluster weighted model (CWM),
which extends the finite mixture of regression model to include modelling of
the covariates. Although many types of distributions have been considered for
both the response and covariates, to our knowledge skewed distributions have
not yet been considered in this paradigm. Herein, a family of 24 novel CWMs are
considered which allows both the covariates and response variables to be
modelled using one of four skewed distributions, or the normal distribution.
Parameter estimation is performed using the expectation-maximization algorithm
and both simulated and real data are used for illustration.
