Nothing better than characteristic function in terms of numerical stability

by Jinhyo Kim and Bongsoo Ko .

Abstract: Numerical handling of the moment generating function (MGF) is seriously sensitive by a small perturbation. Therefore it is hard to implement on a finite-precision digital computer, whereas the characteristic function (CF) is not hard to implement. Algorithm stability is used to support the notion that the CF is superior to the MGF in terms of numerically stable behavior. Furthermore, there cannot exist computationally better tool than CF in terms of numerical stability. Uniqueness of the Vandermonde matrix with the perfect condition number is characterized for the numerical behavior of the CF.

Key Words: moment generating function, characteristic function, condition number, Vandermonde matrix, qualitative computing

Authors:
Jinhyo Kim, jinkim@cheju.cheju.ac.kr
Bongsoo Ko

Editor: John P. Hinde , J.P.Hinde@exeter.ac.uk

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