Large deviations by Poisson approximations (Q1200016)

Some sharp large deviation asymptotics are established for sums of independent, not necessarily identically distributed Bernoulli random variables. As usual, associated (Bernoulli) random variables are introduced via exponential centering. But instead of using a central limit type argument for the latter, a sharper Poisson approximation is applied here. The results are compared to standard approximations, and also simplified versions are presented which avoid numerical technicalities.