Abstract
In this paper, we extend the results obtained in [J. Sunklodas, Some estimates of normal approximation for the distribution of a sum of a random number of independent random variables, Lith. Math. J., 52(3):326–333, 2012] for a thrice-differentiable function h : ℝ → ℝ to the case of h ∈ BL(ℝ); namely, we estimate the quantity | E h(Z N )− E h(Y)| where h is a real bounded Lipschitz function, \( {Z_N}={{{\left( {{S_N}-\mathrm{E}{S_N}} \right)}} \left/ {{\sqrt{{\mathrm{D}{S_N}}}}} \right.} \), S N = X 1 + · · · + X N , X 1 , X 2 , . . . are independent, not necessarily identically distributed, real random variables, N is a positive integer-valued r.v. independent of X 1 , X 2 , . . . , and Y is a standard normal random variable.
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J. Sunklodas, Some estimates of normal approximation for the distribution of a sum of a random number of independent random variables, Lith. Math. J., 52(3):326–333, 2012.
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Sunklodas, J.K. On the normal approximation of a sum of a random number of independent random variables. Lith Math J 52, 435–443 (2012). https://doi.org/10.1007/s10986-012-9185-1
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DOI: https://doi.org/10.1007/s10986-012-9185-1