Abstract
Approximations are very important because it is sometimes not possible to precisely represent exact representation, while in some cases the exact answer is already obtained but is very difficult to apply, as well the approximations sometimes simplify the analytical treatments. Compared with other asymptotic approximations, saddle point approximations have the advantage of always generating probabilities, being very accurate in the tails of the distribution, and being accurate with small samples, sometimes even with only one observation. In this paper, saddle point approximation methods have been proven to be useful for a range of problems, such as the random sum statistics (Poisson-Bernoulli) model which is very complex model.