Name
Title | ||
|---|---|---|
Discretizing distributions with exact moments: Error estimate and convergence analysis |
Abstract | ||
|---|---|---|
We propose a numerical method to approximate a given continuous distribution by a discrete distribution with prescribed moments. The approximation is achieved by minimizing the Kullback-Leibler information of the unknown discrete distribution relative to the known continuous distribution (evaluated at given discrete points) subject to some moment constraints. We study the theoretical error bound and the convergence property of the method. The order of the theoretical error bound of the expectation of any bounded measurable function with respect to the approximating discrete distribution is never worse than the integration formula we start with, and therefore the approximating discrete distribution weakly converges to the given continuous distribution. Moreover, we present some numerical examples that show the advantage of our method. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1063/1.4903706 | AIP Conference Proceedings |
Keywords | Field | DocType |
probability distribution,discrete approximation,generalized moment,integration formula,Kullback-Leibler information,Fenchel duality,error estimate,convergence analysis | Gauss–Kronrod quadrature formula,Continuous function,Discretization,Mathematical optimization,Mathematical analysis,Probability distribution,Quadrature (mathematics),Principle of maximum entropy,Kullback–Leibler divergence,Mathematics,Maximum entropy probability distribution | Journal |
Volume | Issue | ISSN |
1636.0 | 5 | 0094-243X |
Citations | PageRank | References |
0 | 0.34 | 9 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| kenichiro | 1 | 174 | 33.20 |
| Alexis Akira Toda | 2 | 0 | 1.01 |