Executive Summary
Saddle point approximation implementation and derivations have typically relied on tools such as Edgeworth expansions, exponential tilting, complex integration, Hermite polynomials, and other advanced notions. Saddle point approximations are very important tools used in obtaining accurate expressions for distribution functions and densities. It has been a very valuable tool in asymptotic analysis. Since the seminal paper by Daniels (1954), several techniques of accurate approximations that rely on the saddle point approximation on one way or another have been developed. The saddle point approximations, however, derived its concept from the game theory, which involved two suspected criminals under police investigations. The ...