Abstract
The random sum distribution plays a key role in the application of statistics, in addition, it can be used with insurance program, biotechnology and applied medical science. The statistical significance of this distribution arises from its applicability in real life situations. Saddle point approximations are powered tool in obtaining accurate expressions for distribution functions in closed form. Approximations almost outperform other methods with respect to computational costs, though not necessarily with respect to accuracy. However, the paper also, discusses the Saddle point methods to the cumulative distribution function (CDF) for damage process in discrete form. Furthermore, it shows approximations to random sum variable with dependent components assuming presence of the moment generating function (MGF).