We suggest several Chi squared approximations to the distribution of a sum of independent random variables, and derive asymptotic expansions which show that the error of approximation is of order $n^{-1}$ as $n \rightarrow \infty$. The error may be reduced to $n^{-3/2}$ by making a simple secondary approximation.
Publié le : 1983-11-14
Classification:
Approximation,
asymptotic expansion,
central limit theorem,
Chi squared,
rate of convergence,
sums of independent random variables,
60F05,
60G50,
62E20
@article{1176993451,
author = {Hall, Peter},
title = {Chi Squared Approximations to the Distribution of a Sum of Independent Random Variables},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 1028-1036},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993451}
}
Hall, Peter. Chi Squared Approximations to the Distribution of a Sum of Independent Random Variables. Ann. Probab., Tome 11 (1983) no. 4, pp. 1028-1036. http://gdmltest.u-ga.fr/item/1176993451/