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A Generalized Transformed Density Rejection Algorithm

In: Advances in Modeling and Simulation

Author

Listed:
  • Wolfgang Hörmann

    (Boğaziçi University, Department of Industrial Engineering)

  • Josef Leydold

    (Vienna University of Economics and Business, Institute for Statistics and Mathematics)

Abstract

Transformed density rejection is a very flexible method for generating non-uniform random variates. It is based on the acceptance-rejection principle and utilizes a strictly monotone map that transforms the given density into a concave or convex function. Hat function and squeezes are then constructed by means of tangents and secant. We present a new method that works for arbitrary one time continuously differentiable densities. It requires together with the log-density and its derivative a partition of the domain into subdomains that contain at most one inflection point. This improves a previous method of the authors in which also the second derivative is required. We show how the algorithm can be applied to generate from the Generalized Inverse Gaussian distribution, from the Generalized Hyperbolic distribution and from the Watson distribution. The new algorithm can also generate random variates from truncated distributions without problems.

Suggested Citation

  • Wolfgang Hörmann & Josef Leydold, 2022. "A Generalized Transformed Density Rejection Algorithm," Springer Books, in: Zdravko Botev & Alexander Keller & Christiane Lemieux & Bruno Tuffin (ed.), Advances in Modeling and Simulation, pages 283-300, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-10193-9_14
    DOI: 10.1007/978-3-031-10193-9_14
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