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Extreme nth moments for distributions on [0, 1] and the inverse of a moment space map

Published online by Cambridge University Press:  14 July 2016

Morris Skibinsky
Morris Skibinsky*
Affiliation:
University of Massachusetts, Amherst, Mass.
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Extract

Let n be a positive integer. Denote by Mn the convex, closed, bounded, and n-dimensional set of all n-tuples (c1, c2,···, cn) such that for some probability measure a on the Borel subsets of the unit interval I = [0,1].

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 3 , December 1968 , pp. 693 - 701
Copyright
Copyright © Applied Probability Trust 1968 

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References

[1] Aitken, A. C. (1956) Determinants and Matrices. 9th Edition. Oliver and Boyd, London.Google Scholar
[2] Karlin, S. and Shapley, L. S. (1953) Geometry of moment spaces. Mem. Amer. Math. Soc. Number 12.CrossRefGoogle Scholar
[3] Karlin, S. and Studden, W. J. (1966) Tchebycheff Systems: With Applications in Analysis and Statistics. Interscience Publishers, New York.Google Scholar
[4] Skibinsky, M. (1967) The range of the (n + 1)th moment for distributions on [0, 1]. J. Appl. Prob. 4, 543–552.Google Scholar