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.
Mots-clés : multiply monotonicity, symmetric densities, unimodality, Wintner's theorem, Bernstein's inequality
@article{PS_2013__17__605_0, author = {Lef\`evre, Claude and Utev, Sergey}, title = {Convolution property and exponential bounds for symmetric monotone densities}, journal = {ESAIM: Probability and Statistics}, pages = {605--613}, publisher = {EDP-Sciences}, volume = {17}, year = {2013}, doi = {10.1051/ps/2012012}, mrnumber = {3085635}, zbl = {1291.60030}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2012012/} }
TY - JOUR AU - Lefèvre, Claude AU - Utev, Sergey TI - Convolution property and exponential bounds for symmetric monotone densities JO - ESAIM: Probability and Statistics PY - 2013 SP - 605 EP - 613 VL - 17 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2012012/ DO - 10.1051/ps/2012012 LA - en ID - PS_2013__17__605_0 ER -
%0 Journal Article %A Lefèvre, Claude %A Utev, Sergey %T Convolution property and exponential bounds for symmetric monotone densities %J ESAIM: Probability and Statistics %D 2013 %P 605-613 %V 17 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2012012/ %R 10.1051/ps/2012012 %G en %F PS_2013__17__605_0
Lefèvre, Claude; Utev, Sergey. Convolution property and exponential bounds for symmetric monotone densities. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 605-613. doi : 10.1051/ps/2012012. http://www.numdam.org/articles/10.1051/ps/2012012/
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