Titlebook: Series Approximation Methods in Statistics; John E. Kolassa Book 19941st edition Springer Science+Business Media New York 1994 Area.approx

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Saddlepoint Series for Distribution Functions,s for the density is a linear combination of derivatives of the normal distribution function, and hence is easily integrated to give a corresponding cumulative distribution function approximation. This cumulative distribution function approximation inherits many good properties from the density approximation.

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Asymptotics in General,stributions of random variables, including theorems concerning convergence almost surely, to many questions in applied statistics. Le Cam (1969) treats asymptotics from a decision-theoretic viewpoint. Barndorff-Nielsen and Cox (1989) present many applications of the density and distribution function

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Characteristic Functions and the Berry-Esseen Theorem,unction to be reconstructed from the characteristic function are presented. Results are also derived outlining the sense in which inversion of an approximate characteristic function leads to an approximate density or distribution function. These results are applied to derive Berry—Esseen theorems qu

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Edgeworth Series,teristic function, and that many of its properties could be described in terms of the first few derivatives of the characteristic function at 0. This chapter considers higher-order approximations to cumulative distribution functions and densities. Not surprisingly, these can also be expressed as app

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