Approximations for sums of three-valued 1-dependent symmetric random variables

Abstract

The sum of symmetric three-point 1-dependent nonidentically distributed random variables is approximated by a compound Poisson distribution. The accuracy of approximation is estimated in the local and total variation norms. For distributions uniformly bounded from zero, the accuracy of approximation is of the order O(n–1). In the general case of triangular arrays of identically distributed summands, the accuracy is at least of the order O(n–1/2). Nonuniform estimates are obtained for distribution functions and probabilities. The characteristic function method is used.

Keywords

• compound Poisson distribution
• 1-dependent variables
• total variation norm
• local norm
• nonuniform estimate