fourierin: An R package to compute Fourier integrals

Guillermo Basulto-Elias, Alicia Carriquiry, Kris,De Brabanter, Daniel,J. Nordman
<span title="">2017</span> <i title="The R Foundation"> <a target="_blank" rel="noopener" href="" style="color: black;">The R Journal</a> </i> &nbsp;
We present the R package fourierin (Basulto-Elias, 2017) for evaluating functions defined as Fourier-type integrals over a collection of argument values. The integrals are finitely supported with integrands involving continuous functions of one or two variables. As an important application, such Fourier integrals arise in so-called "inversion formulas", where one seeks to evaluate a probability density at a series of points from a given characteristic function (or vice versa) through Fourier
more &raquo; ... nsforms. This paper intends to fill a gap in current R software, where tools for repeated evaluation of functions as Fourier integrals are not directly available. We implement two approaches for such computations with numerical integration. In particular, if the argument collection for evaluation corresponds to a regular grid, then an algorithm from Inverarity (2002) may be employed based on a fast Fourier transform, which creates significant improvements in the speed over a second approach to numerical Fourier integration (where the latter also applies to cases where the points for evaluation are not on a grid). We illustrate the package with the computation of probability densities and characteristic functions through Fourier integrals/transforms, for both univariate and bivariate examples.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.32614/rj-2017-044</a> <a target="_blank" rel="external noopener" href="">fatcat:3s26tlvq4fc4dkyab42z7fbcde</a> </span>
<a target="_blank" rel="noopener" href="" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href=""> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / </button> </a>