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We obtain nonuniform and quasi-nonuniform estimates, where the "main" summand under wide assumptions is equivalent to the difference of distribution functions. The construction of these estimates is given with the help of asymptotic expansions. [ABSTRACT FROM AUTHOR]

We obtained several quasi-nonuniform estimates for the residuals of the Bergström-Chebyshev expansion for densities of normalized sums of n independent identically distributed random variables, i.e., of the estimates whose uniform terms decrease faster than nonuniform ones as n→∞. [ABSTRACT FROM AUTHOR]

The structure of the nonuniform estimate of convergence rate in the local central limit theorem for the densities of sums of independent identically distributed random variables is made more accurate. The absolute constants are written out explicitly. [ABSTRACT FROM AUTHOR]