Hausdorff moment problem and Maximum Entropy: On the existence conditions
Section snippets
Hausdorff moment problem and Maximum Entropy
The finite Hausdorff moment problem consists of recovering an unknown probability density function (pdf) f(x), with support D = [0, 1], from the knowledge of its associated sequence of integer moments, with . In actual practice, the problem consists of determining approximations to the unknown underlying function f(x) from a finite collection of its integer moments. Then we settle for a reasonable analytical form of f(x), and the Maximum Entropy (MaxEnt)
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Novel algorithm for reconstruction of a distribution by fitting its first-four statistical moments
2019, Applied Mathematical ModellingCitation Excerpt :It is known that the PDF can be uniquely determined if a infinite number of statistical moments are provided, which are always unavailable in practices. Instead, a reduced number of statistical moments are always used for the reconstruction of the PDF, which leads to the so-called classical moment problem [1–3]. That is, the reconstruction of a PDF using a finite number of its statistical moments could be an ill-posed inverse problem, where the existence and the uniqueness of the PDF may be questioned.
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