Masters Degrees (Statistics and Actuarial Science)
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Browsing Masters Degrees (Statistics and Actuarial Science) by Author "Buitendag, Sven"
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- ItemThe saddle-point method and its application to the hill estimator(Stellenbosch : Stellenbosch University, 2016-12) Buitendag, Sven; De Wet, Tertius; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics & Actuarial Science.ENGLISH SUMMARY : 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.