Large deviation local limit theorems for ratio statistics

Let ;Under some mild and easily verifiable conditions on ;When ;We also present the corresponding results for the ratio of sums of i.i.d. random variables along with some interesting applications. In all of these applications, the p.d.f.'s (or p.m.f.'s) do not have closed form expressions. However, our results provide simple computable approximations involving moment generating functions for such p.d.f.'s (or p.m.f.'s). We verify our result for the F statistic, whose exact density is available. Our approximation coincides with the exact expression except for the normalizing constant. However, we show that our approximation is asymptotically equivalent to the exact density.;Let...