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Characteristic Functions and the Berry-Esseen Theorem

  • John E. Kolassa
Part of the Lecture Notes in Statistics book series (LNS, volume 88)

Abstract

This chapter discusses the role of the characteristic function in describing probability distributions. Theorems allowing the underlying probability function 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 quantifying the error incurred in such an approximation. Finally, the relation between the characteristic function and moments and cumulants are investigated.

Keywords

Characteristic Function Cumulative Distribution Function Lattice Distribution Moment Generate Function Cumulant Generate Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • John E. Kolassa
    • 1
  1. 1.Department of BiostatisticsUniversity of Rochester, School of Medicine and DentistryRochesterUSA

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