Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-29T15:22:53.419Z Has data issue: false hasContentIssue false
  • English
  • Français

Jensen's inequality for distributions possessing higher moments, with application to sharp bounds for Laplace-Stieltjes transforms

Published online by Cambridge University Press:  17 February 2009

B. Guljaš ,
C. E. M. Pearce  and
J. Pečarić
B. Guljaš
Affiliation:
Mathematics Department, University of Zagreb, Bijenička Cesta 30, 41000 Zagreb, Croatia
C. E. M. Pearce
Affiliation:
Department of Applied Mathematics, The University of Adelaide, Adelaide SA 5005, Australia.
J. Pečarić
Affiliation:
Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 41000 Zagreb, Croatia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A new version of Jensen's inequality is established for probability distributions on the non-negative real numbers which are characterized by moments higher than the first. We deduce some new sharp bounds for Laplace-Stieltjes transforms of such distribution functions.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 1 , July 1998 , pp. 80 - 85
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Aumann, G. and Haupt, O., Einführung in die Reelle Analysis, Band II (Walter de Gruyter, Berlin, 1938).Google Scholar
[2]Bullen, P. S., “A criterion for n-convexity”, Pacific J. Math. 36 (1971) 81–98.CrossRefGoogle Scholar
[3]Eckberg, A. E., “Sharp bounds on Laplace-Stieltjes transforms, with applications to various queueing problems”, Math. of Oper Res. 2 (1977) 135–142.CrossRefGoogle Scholar
[4]Pearce, C. E. M. and Pečarić, J. E., “An integral inequality for convex functions, with application to teletraffic congestion problems”, Math. of Oper. Res. 20 (1995) 526–528.CrossRefGoogle Scholar
[5]Pečarić, J. E., Proschan, F. and Tong, Y. L., Convex functions, partial orderings and statistical applications. Mathematics in Science and Engineering, Vol. 187 (Academic Press, San Diego, 1992).Google Scholar
[6]Pittenger, A. O., “Sharp mean-variance bounds for Jensen-type inequalities”, Probability and Statistics Letters 10 (1990) 91–94.CrossRefGoogle Scholar
[7]Popoviciu, T., Les fonctions convexes (Hermann, Paris, 1945).Google Scholar
[8]Rolski, T., “Some inequalities for GI/M/n queues”, Zastos. Mat. 13 (1972) 43–47.Google Scholar