Entropy estimate of probability densities having assigned moments: Hausdorff case

Applied Mathematics Letters

Volumn 15, Issue 3, 2002, Pages 309-314

  Tagliani, A ^a  

^a UNIVERSITY OF TRENTO   (Italy)

Author keywords

Convex hull; Entropy; Hankel matrix; Moment problem

Indexed keywords

EID: 31244431547     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(01)00136-7     Document Type: Article

References (11)

1. E.T. Jaynes, Where do we stand on maximum entropy, In The Maximum Entropy Formalism, (Edited by R.D. Levine and M. Tribus), pp. 15-118, MIT Press, Cambridge, MA, (1978).
2. J.A. Shohat and J.D. Tamarkin, The Problem of Moments, Volume 1, AMS Mathematical Survey, Providence, RI, (1943).
3. I. Csiszar, I-divergence geometry of probability distributions and minimization problems, The Annals of Probability 1, 146-158 (1975).
4. J.M. Borwein and A.S. Lewis, Convergence of best entropy estimate, SIAM J. Optimization 1, 191-205 (1991).
5. A. Tagliani, Hausdorff moment problem and maximum entropy: A unified approach, Applied Math. and Computation 105, 291-305 (1999).
6. C. Jardas, J. Pecaric, R. Roki and N. Sarapa, On some inequalities for entropies of discrete probability distributions, J. Australian Mathematical Society, Ser. B, 40, 535-541 (1999).
7. T.M. Cover and J.A. Thomas, Elements of Information Theory, John Wiley & Sons, (1991).
8. E.E. Tyrtyshnikov, How bad are Hankel matrices?, Numerische Mathematics 67, 261-269 (1994).
9. H.K. Kesavan and J.N. Kapur, Entropy Optimization Principles with Applications, Academic Press, (1992).
10. S. Karlin and L.S. Shapley, Geometry of Moment Spaces, Volume 12, AMS Memoirs, Providence, RI, (1953).
11. D. Fasino, The spectral properties of Hankel matrices and numerical solution of finite moment problem, J. of Computational and Applied Mathematics 65, 145-155 (1995).