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Generalized Hausdorff inverse moment problem

✍ Scribed by María B. Pintarelli; Fernando Vericat

Book ID
104340780
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
249 KB
Volume
324
Category
Article
ISSN
0378-4371

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✦ Synopsis

We consider a generalization of Hausdor moment problem in which the inputs are generalized moments deÿned by n ≡ 1 0 x n [f(x)] d x (n = 1; 2; : : :) where is a real number and f(x) is the probability density function to be determined. The necessary and su cient conditions for the existence of the solution are established. The convergence of the sequence of solutions for the corresponding ÿnite problem, when the number of input moments increases, is also studied. We show how to construct this sequence by using a maximum-entropy principle which is based on Tsallis's family of entropies. The method is illustrated with a number of examples.

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