Abstract:
The sums of independent identically distributed random variables
having a lattice distribution are
considered. It is assumed that the unilateral Cramer condition
holds in a bounded interval $(0,\lambda)$, that is, the extreme
right conjugate distribution does not exist. Under an additional
assumption on the regularity of the right tail of the underlying
distribution, the local and integral theorems on large deviations
of an arbitrarily high order are established.