|Serge B Provost (Canada)||email@example.com|
It is often the case that the moments of a distribution can be readily determined, while its exact density function is mathematically intractable. We show that the density function of a continuous distribution defined on a closed interval can be easily approximated from its exact moments by solving a linear system involving a Hilbert matrix. When sample moments are being used, the same linear system will yield density estimates. A simple formula that is based on an explicit representation of the elements of the inverse of a Hilbert matrix is being proposed as a means of directly determining density estimates or approximants without having to resort to kernels or orthogonal polynomials. As illustrations, density estimates will be determined for the `Buffalo snowfallŽ data set and the density of the distance between two random points in a cube will be approximated. Finally, an alternate methodology is proposed for obtaining smooth density estimates from averaged shifted histograms.
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