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Generalized Hausdorff inverse moment problem

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  • Pintarelli, María B.
  • Vericat, Fernando

Abstract

We consider a generalization of Hausdorff moment problem in which the inputs are generalized moments defined by μαn≡∫01xn[f(x)]αdx(n=1,2,…) where α is a real number and f(x) is the probability density function to be determined. The necessary and sufficient conditions for the existence of the solution are established. The convergence of the sequence of solutions for the corresponding finite 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.

Suggested Citation

  • Pintarelli, María B. & Vericat, Fernando, 2003. "Generalized Hausdorff inverse moment problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 568-588.
    • Handle: RePEc:eee:phsmap:v:324:y:2003:i:3:p:568-588
    DOI: 10.1016/S0378-4371(03)00066-9
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    References listed on IDEAS

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    1. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
    2. Plastino, A.R. & Plastino, A., 1994. "Dynamical aspects of Tsallis' entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(3), pages 438-448.
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