Fourier transformation can improve quadrature efficiency of Laplace distribution

Jinhyo Kim and Sangwon Seo
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Jinhyo Kim: Cheju National University
Sangwon Seo: Seoul National University

Computational Statistics, 2001, vol. 16, issue 2, No 2, 233-242

Abstract: 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.

Keywords: Fourier transformation; Gauss-Hermite quadrature; Laplace distribution; Cauchy distribution (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/s001800100062

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