Voir la notice de l'article provenant de la source Numdam
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.
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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
Cité par Sources :