This paper discusses three families of flexible parametric probability density functions: the skewed generalized t, the exponential generalized beta of the second kind, and the inverse hyperbolic sin distributions. These families allow quite flexible modeling the first four moments of a distribution and could be considered in modeling a wide variety of economic problems. We illustrate their use in a simple regression model with a simulation study that demonstrates that the use of the flexible distributions may result in significant efficiency gains relative to more conventional regression procedures, such as ordinary least squares or least absolute deviations regression, without a suffering from a large efficiency loss when errors are Gaussian.