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Convolution property and exponential boundsfor symmetric monotone densities

Published online by Cambridge University Press:  06 August 2013

Claude Lefèvre
Affiliation:
Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, 1050 Bruxelles, Belgique. [email protected]
Sergey Utev
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, NG7 2RD Nottingham, UK; [email protected]
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Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2013

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