  Assuming an exponential power distribution is one way to deal with outliers
in regression and clustering, which can increase the robustness of the
analysis. Gaussian distribution is a special case of an exponential
distribution. And an exponential power distribution can be viewed as a scale
mixture of normal distributions. Thus, model selection methods developed for
the Gaussian mixture model can be easily extended for the exponential power
mixture model. Moreover, Gaussian mixture models tend to select more components
than exponential power mixture models in real-world cases, which means
exponential power mixture models are easier to interpret. In this paper, We
develop analyses for mixture regression models when the errors are assumed to
follow an exponential power distribution. It will be robust to outliers, and
model selection for it is easy to implement.
