The saddle-point method and its application to the hill estimator

The saddle-point approximation is a highly accurate approximation of the distribution of a random variable. It was originally derived as an approximation in situations where a parameter takes on large values. However, due to its high accuracy and good behaviour in a variety of applications not involving such a parameter, it has been generalized and applied to the distribution of any random variable with a well-behaved cumulant generating function. In this thesis the theory underlying the saddle-point approximation will be discussed and illustrated with an application to approximate the distribution of the Hill estimator in extreme value theory.National Research Foundatio