Estimates for the variational distance between two sets of independent random variables

We obtain explicit lower and upper estimates of the total variation distance between distributions of two sets $(X_1,\ldots,X_n)$ and $(Y_1,\ldots,Y_n)$ of independent random variables which may be nonidentically distributed inside each set. Estimates are formulated in terms of total variation distances $\rho_k$ between distributions of separate components $X_k$ and $Y_k$, $k=1,\ldots,n$. Results for the case of homogeneous samples was considered in this journal in 2018. On the qualitative level the estimates of the present paper correspond with the estimates obtained for the homogeneous cases earlier.