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UBC Theses and Dissertations

Saddlepoint approximations to distribution functions Hauschildt, Reimar

Abstract

In this thesis we present two approximations to the distribution function of the sum of n independent random variables. They are obtained from generalizations of asymptotic expansions derived by Rubin and Zidek who considered the case of chi random variables. These expansions are obtained from Gurland's inversion formula for the distribution function by using an adaptation of Laplace's method for integrals. By means of numerical results obtained for a variety of common distributions and small values of n these approximations arc compared to the classical methods of Edgeworth and Cramer. Finally, the method is used to obtain approximations to the non-central chi-square distribution and to the doubly non-central F-distribution for various cases defined in terms of its parameters.

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