On the rate of convergence to bivariate stable laws

In the paper, we approximate the distribution function of a sum of independent nonidentically distributed bivariate random vectors by the distribution function of a stable vector and estimate the accuracy of such an approximation. The obtained general result is only a little bit worse when compared with known estimates for the case of multivariate independent and identically distributed random vectors or univariate nonidentically distributed summands. We also apply the result obtained to a specific scheme arising when considering the so-called Increment-Ratio Statistics.