An inequality for
probability density functions arising from a distinguishability problem
Boris Guljas
Department of Mathematics, University of Zagreb
Bijenicka c. 30, 41000 Zagreb, Croatia
and
C. E. M. Pearce
Department of Applied Mathematics
The University of Adelaide
Adelaide SA 5005, Australia
and
Josip Pecaric
Faculty of Textile Technology,University of Zagreb
Pierottijeva 6, 41000 Zagreb, Croatia
Abstract:
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
and
.
PDF file size:
© Copyright 1998, Australian Mathematical Society
TeXAdel Scientific Publishing
26/04/2000
![\begin{displaymath}\int_{-\infty}^{+\infty} \frac{[f^{\prime}(x)^2]^{\gamma\alph...
...(x)\vert^{\alpha-1}}
{[f(x)]^{\beta-\alpha}}dx\right)^{\gamma}
\end{displaymath}](img1.gif){kind=small}