The Fourier-series method for inverting transforms of probability distributions

@article{Abate1992TheFM,
  title={The Fourier-series method for inverting transforms of probability distributions},
  author={Joseph Abate and Ward Whitt},
  journal={Queueing Systems},
  year={1992},
  volume={10},
  pages={5-87}
}
This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourier-series method are remarkably easy to use, requiring programs of less than fifty lines. The Fourier-series method can be interpreted as numerically integrating a standard inversion integral by means of the trapezoidal rule. The same… 

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