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Convolution property and exponential boundsfor symmetric monotone densities

Published online by Cambridge University Press:  06 August 2013

Claude Lefèvre  and
Sergey Utev
Claude Lefèvre
Affiliation:
Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, 1050 Bruxelles, Belgique. clefevre@ulb.ac.be
Sergey Utev
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, NG7 2RD Nottingham, UK; sergey.utev@nottingham.ac.uk
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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.

Keywords

Multiply monotonicitysymmetric densitiesunimodalityWintner’s theoremBernstein’s inequality

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 605 - 613
Copyright
© EDP Sciences, SMAI, 2013

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