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An inequality for probability density functions arising from a distinguishability problem
Published online by Cambridge University Press: 17 February 2009
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 β > α 1 and 1/(β+1) < γ ≤ 1.
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- Copyright © Australian Mathematical Society 1998