Sharp upper bounds are offered for the total variation distance between the distribution of a sum of independent random variables following a skewed distribution with an absolutely continuous part, and an appropriate shifted gamma distribution. These bounds vanish at a rate as while the corresponding distance to the normal distribution vanishes at a rate implying that, for skewed summands, pre-asymptotic (penultimate) gamma approximation is much more accurate than the usual normal approximation. Two illustrative examples concerning lognormal and Pareto summands are presented along with numerical comparisons confirming the aforementioned ascertainment.
DOI : 10.1051/ps/2015010
Mots-clés : Central limit theorem, gamma approximation, lognormal sums, rates of convergence, Pareto sums, total variation distance, quantile approximation
@article{PS_2015__19__590_0, author = {Boutsikas, Michael V.}, title = {Penultimate gamma approximation in the {CLT} for skewed distributions}, journal = {ESAIM: Probability and Statistics}, pages = {590--604}, publisher = {EDP-Sciences}, volume = {19}, year = {2015}, doi = {10.1051/ps/2015010}, mrnumber = {3433428}, zbl = {1333.60027}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps/2015010/} }
TY - JOUR AU - Boutsikas, Michael V. TI - Penultimate gamma approximation in the CLT for skewed distributions JO - ESAIM: Probability and Statistics PY - 2015 SP - 590 EP - 604 VL - 19 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2015010/ DO - 10.1051/ps/2015010 LA - en ID - PS_2015__19__590_0 ER -
%0 Journal Article %A Boutsikas, Michael V. %T Penultimate gamma approximation in the CLT for skewed distributions %J ESAIM: Probability and Statistics %D 2015 %P 590-604 %V 19 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2015010/ %R 10.1051/ps/2015010 %G en %F PS_2015__19__590_0
Boutsikas, Michael V. Penultimate gamma approximation in the CLT for skewed distributions. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 590-604. doi : 10.1051/ps/2015010. http://archive.numdam.org/articles/10.1051/ps/2015010/
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