Abstract
Points can be generated uniformly in a compact setA ofR d by constructing a fine rectangular grid coveringA, selecting a grid rectangle, and performing an acceptance test if the rectangle in question is not entirely contained inA. For very fine grids, the acceptance test is needed with very small probability. We look at the storage requirements and expected time performance of this method, and apply it in avoidance problems and in the design of fast generators for random variates with a bounded density on [0, 1].
Zusammenfassung
Punkte, die in einer komplexen TeilmengeA vonR d gleich verteilt sind, können auf folgende Weise erzeugt werden: Wir überdeckenA mit einem engmaschigen Rechteckgitter und führen einen Annahmetest aus, wenn das betrachtete Rechteck nicht zur Gänze inA enthalten ist. Für sehr engmaschige Gitter wird dieser Annahmetest mit sehr kleiner Wahrscheinlichkeit aufgerufen. Wir untersuchen den Speicherbedarf und die mittlere Zeitkomplexität dieser Methode und wenden das Verfahren auf Probleme mit verbotenen Teilmengen und auf schnelle Generatoren für Zufallsveränderliche mit beschränkter Dichte in [0, 1] an.
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Devroye, L. Grid methods in simulation and random variate generation. Computing 37, 71–84 (1986). https://doi.org/10.1007/BF02252735
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DOI: https://doi.org/10.1007/BF02252735