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Convolution property and exponential boundsfor symmetric monotone densities
Published online by Cambridge University Press: 06 August 2013
Abstract
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Our first theorem states that the convolution of two symmetric densities which are k-monotone on (0,∞) is again (symmetric) k-monotone provided 0 < k ≤ 1. We then apply this result, together with an extremality approach, to derive sharp moment and exponential bounds for distributions having such shape constrained densities.
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- © EDP Sciences, SMAI, 2013
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