Asymptotic expansions for distribution of sums quasi-lattice random variables

Abstract

Althoug Chebyshev [3] and Edeworth [5] had conceived of the formal expansions for distribution of sums of independent random variables, but only in Cramer’s work [4] was laid a proper foundation of this problem. In the case when random variables are lattice Esseen get the asymptotic expansion in a new different form. Here we extend this problem for quasi-lattice random variables.

Keywords

• Edgeworth expansions
• quasi-lattice distributions
• Esseen expansions