  Myerson's regularity condition of a distribution is a standard assumption in
economics. In this paper, we study the complexity of describing a regular
distribution within a small statistical distance. Our main result is that
$\tilde{\Theta}{(\epsilon^{-0.5})}$ bits are necessary and sufficient to
describe a regular distribution with support $[0,1]$ within $\epsilon$ Levy
distance. We prove this by showing that we can learn the regular distribution
approximately with $\tilde{O}(\epsilon^{-0.5})$ queries to the cumulative
density function. As a corollary, we show that the pricing query complexity to
learn the class of regular distribution with support $[0,1]$ within $\epsilon$
Levy distance is $\tilde{\Theta}{(\epsilon^{-2.5})}$. To learn the mixture of
two regular distributions, $\tilde{\Theta}(\epsilon^{-3})$ pricing queries are
required.
