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An inequality for probability density functions arising from a distinguishability problem

Published online by Cambridge University Press:  17 February 2009

Boris Guljaš ,
C. E. M. Pearce  and
Josip Pečarić
Boris Guljaš
Affiliation:
Department of Mathematics, University of Zagreb, Bijenička c. 30, 41000 Zagreb, Croatia
C. E. M. Pearce
Affiliation:
Department of Applied Mathematics, The University of Adelaide, Adelaide SA 5005, Australia
Josip Pečarić
Affiliation:
Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 41000 Zagreb, Croatia
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Abstract

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An integral inequality is established involving a probability density function on the real line and its first two derivatives. This generalizes an earlier result of Sato and Watari. If f denotes the probability density function concerned, the inequality we prove is that

under the conditions β > α 1 and 1/(β+1) < γ ≤ 1.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 3 , January 1998 , pp. 350 - 354
Copyright
Copyright © Australian Mathematical Society 1998

References

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