The Automatic Generation of One- and Multi-dimensional Distributions with Transformed Density Rejection

Josef Leydold; Wolfgang Hörmann

doi:10.57938/f974a6f7-d13a-4358-8b95-db67f0fe3e16

The Automatic Generation of One- and Multi-dimensional Distributions with Transformed Density Rejection

Josef Leydold
, Wolfgang Hörmann

Institute for Statistics and Mathematics

Publication: Working/Discussion Paper › WU Working Paper and Case

27 Downloads (Pure)

Abstract

A rejection algorithm, called ``transformed density rejection", is presented. It uses a new method for constructing simple hat functions for a unimodal density $f$. It is based on the idea of transforming $f$ with a suitable transformation $T$ such that $T(f(x))$ is concave. The hat function is then constructed by taking the pointwise minimum of tangents which are transformed back to the original scale. The resulting algorithm works very well for a large class of distributions and is fast. The method is also extended to the two- and multidimensional case. (author's abstract)

Original language	English
Place of Publication	Vienna
Publisher	Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business
DOIs	https://doi.org/10.57938/f974a6f7-d13a-4358-8b95-db67f0fe3e16
Publication status	Published - 1997

Publication series

Series	Preprint Series / Department of Applied Statistics and Data Processing
Number	20

WU Working Papes and Cases

Preprint Series / Department of Applied Statistics and Data Processing

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10.57938/f974a6f7-d13a-4358-8b95-db67f0fe3e16Licence: Unspecified

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Cite this

Leydold, J., & Hörmann, W. (1997). The Automatic Generation of One- and Multi-dimensional Distributions with Transformed Density Rejection. (June 1997 ed.) Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business. Preprint Series / Department of Applied Statistics and Data Processing No. 20 https://doi.org/10.57938/f974a6f7-d13a-4358-8b95-db67f0fe3e16

Leydold, Josef ; Hörmann, Wolfgang. / The Automatic Generation of One- and Multi-dimensional Distributions with Transformed Density Rejection. June 1997. ed. Vienna : Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, 1997. (Preprint Series / Department of Applied Statistics and Data Processing; No. 20).

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Leydold, J & Hörmann, W 1997 'The Automatic Generation of One- and Multi-dimensional Distributions with Transformed Density Rejection' Preprint Series / Department of Applied Statistics and Data Processing, no. 20, June 1997 edn, Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, Vienna. https://doi.org/10.57938/f974a6f7-d13a-4358-8b95-db67f0fe3e16

The Automatic Generation of One- and Multi-dimensional Distributions with Transformed Density Rejection. / Leydold, Josef; Hörmann, Wolfgang.
June 1997. ed. Vienna: Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, 1997.

Publication: Working/Discussion Paper › WU Working Paper and Case

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