Volume 17, 2013
|Page(s)||605 - 613|
|Published online||06 August 2013|
Convolution property and exponential bounds for symmetric monotone densities
1 Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, 1050 Bruxelles, Belgique
2 School of Mathematical Sciences, University of Nottingham, University Park, NG7 2 RD Nottingham, UK
Received: 15 June 2011
Revised: 13 April 2012
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.
Mathematics Subject Classification: 60E10 / 60E15
Key words: Multiply monotonicity / symmetric densities / unimodality / Wintner’s theorem / Bernstein’s inequality
© EDP Sciences, SMAI, 2013
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