Asymptotics of optimal quantizers for some scalar distributions

TitleAsymptotics of optimal quantizers for some scalar distributions
Publication TypeJournal Article
Year of Publication2002
AuthorsJean-Claude Fort, and Gilles Pagès
JournalJ. Comput. Appl. Math.

We obtain semi-closed forms for the optimal quantizers of some families of one-dimensional probability distributions. They yield the first examples of non-log-concave distributions for which uniqueness holds. We give two types of applications of these results. One is a fast computation of numerical approximations of one-dimensional optimal quantizers and their use in a multidimensional framework. The other is some asymptotics of the standard empirical measures associated to the optimal quantizers in terms of distribution function, Laplace transform and characteristic function. Moreover, we obtain the rate of convergence in the Bucklew & Wise Theorem and finally the asymptotic size of the Voronoi tessels.