Description Complexity of Regular Distributions
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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 Θ̃(ϵ^-0.5) bits are necessary and sufficient to describe a regular distribution with support [0,1] within ϵ Levy distance. We prove this by showing that we can learn the regular distribution approximately with Õ(ϵ^-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 ϵ Levy distance is Θ̃(ϵ^-2.5). To learn the mixture of two regular distributions, Θ̃(ϵ^-3) pricing queries are required.
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