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Hausdorff Moment Transforms and Their Performance

Xinyun WangMartin Haenggi
Dec 2022
摘要
Various methods have been proposed to approximate a solution to the truncatedHausdorff moment problem. In this paper, we establish a method of comparisonfor the performance of the approximations. Three ways of producing randommoment sequences are discussed and applied. Also, some of the approximationshave been rewritten as linear transforms and detailed accuracy requirements areanalyzed. Our finding shows that the performance of the approximations differssignificantly in their convergence properties, accuracy, and numericalcomplexity, and that the decay type of the moment sequence strongly affects theaccuracy requirement.
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