摘要: Let X = Pn i=1 aiξi be a Rademacher sum with V ar(X) = 1 and Z be a standard normal random variable. This paper concerns the upper bound of |P(X ≤ x) ? P(Z ≤ x)| for any x ∈ R. Using the symmetric properties and R software, this paper gets the following improved Berry Esseen type bound under some conditions, |P(X ≤ x) ? P(Z ≤ x)| ≤ P Z ∈ (0, a1)
, ?x ∈ R, which is one of the conjecture proposed by Nathan K. and Ohad