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Fourier transformation can improve quadrature efficiency of Laplace distribution

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Summary

A numerical quadrature of a particular probability integral is concerned with using the Fourier transformation which smoothes the stiffness. The Fourier transformation of the Laplace distribution becomes, in a statistical sense, the Cauchy distribution. It is shown that the Gauss-Hermite quadrature of the Cauchy distribution, equivalent to the Fourier-transformed Laplace distribution, exhibits better numerical efficiency than the Gauss-Hermite quadrature of the untransformed Laplace distribution. A numerical example supports the analytic argument.

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Authors and Affiliations

  1. Department of Computer Sciences and Statistics, Cheju National University, Cheju, 690-756, Korea

    Jinhyo Kim

  2. Department of Mathematics, Seoul National University, Seoul, 151-742, Korea

    Sangwon Seo

Authors
  1. Jinhyo Kim
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  2. Sangwon Seo
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Additional information

This research was supported by the Brain Korea 21 Project.

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Kim, J., Seo, S. Fourier transformation can improve quadrature efficiency of Laplace distribution. Computational Statistics 16, 233–242 (2001). https://doi.org/10.1007/s001800100062

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