Nothing better than characteristic function in terms of numerical stability
by Jinhyo Kim and Bongsoo Ko
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.
moment generating function, characteristic function,
condition number, Vandermonde matrix, qualitative computing
John P. Hinde
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