Hausdorff moment problem and fractional moments (Q984383)

In probabilistic terms, the Hausdorff moment problem means to recover an unknown probability density function \(f\in L^2[0,1]\) from the knowledge of its associated sequence \(\{\mu_j\}^M_{j=0}\) of integer moments, that is, \(\mu_j=\int_0^1x^jf(x),j\geq0,\mu_0=1\). The authors propose a solution to the Hausdorff moment problem using fractional moments, appropriately chosen, of the form \(\int_0^1x^{\alpha}f(x)dx\), with \(\alpha\in\mathbb R^+\). Fractional moments are computed from integer moments via so-called centered moments. They are used in turn to solve finite Hausdorff moment problems by means of a maximum entropy technique, and in authors' opinion, they represent a remedy to ill-conditioning coming from a high number of integer moments needed by the recovering procedure.