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Approximations for the Distribution Function of the Sum of iid Random Variables with Compact Support in R+

Please always quote using this URN: urn:nbn:de:0297-zib-1990
  • In this paper a unified approach to central and decentral approximations of the distribution function $F(x,n)$ of the sum of $n$ iid random variables with compact support in $I\!\!R_+$ is given. This approach yields direct Edgeworth expansion (especially the Central limit theorem) and indirect Edgeworth expansion (Theorem of Bahadur-Rao, large deviation results) within a unified framework. An approximative inversion of the LST of $F(x,n)$ (approximation of the complex inversion integral over a line by an integral over a proper bounded arc with a proper integrand) allows to get these approximations and moreover explicit error bounds.

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Metadaten
Author:Manfred Brandt
Document Type:ZIB-Report
Date of first Publication:1995/11/30
Series (Serial Number):ZIB-Report (SC-95-33)
ZIB-Reportnumber:SC-95-33
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