Estimates of the Rate of Convergence in the Limit Theorem for Negative Binomial Random Sums.

New practically applicable estimates are constructed for the accuracy of approximation to the distributions of negative binomial random sums in the case where the shape parameter r > 0 of the negative binomial distribution satisfies the condition r ⩽ δ/2, where 2 + δ is the maximum order of the moment of random summands, δ ∈ (0, 1]. [ABSTRACT FROM AUTHOR]