Abstract:
We consider various approximations in the central limit theorem for distributions of sums of independent random variables. We study how many summands in the normalized sums guarantee the precision 10−3 for these approximations. It turns out that for the same distribution but different approximations this number varies from hundreds of thousands to a few tens.
Keywords:
central limit theorem, accuracy of approximation, asymptotic expansions.
Citation:
V. V. Senatov, “On the real accuracy of approximation in the central limit theorem”, Sibirsk. Mat. Zh., 52:4 (2011), 913–935; Siberian Math. J., 52:4 (2011), 727–746