## Simulating the Dickman distribution

Venue: | Statist. Probab. Lett |

Citations: | 5 - 0 self |

### BibTeX

@ARTICLE{Devroye_simulatingthe,

author = {Luc Devroye and Omar Fawzi},

title = {Simulating the Dickman distribution},

journal = {Statist. Probab. Lett},

year = {},

pages = {242--247}

}

### OpenURL

### Abstract

Abstract. In this paper, we give a simple algorithm for sampling from the Dickman distribution. It is based on coupling from the past with a suitable dominating Markov chain.

### Citations

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Citation Context ...06); Nietlispach (2007); Penrose and Wade (2004); Takács (1955); Vervaat (1979). These are special cases of more general random variables that may be written as A0 + A1W1 + A2W1W2 + A3W1W2W3 + · · · (=-=Embrechts et al., 1997-=-, section 8.4) and that occur as solutions of random recurrence relations or in financial mathematics. The special case of a Vervaat perpetuity occurs when W = U 1/β , β > 0, where U is a uniform [0, ... |

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Citation Context ...ted using a simple update function g. Coupling from the past cannot be applied directly to this Markov chain because it is not uniformly ergodic, which basically means that coalescence cannot happen (=-=Foss and Tweedie, 1998-=-). In Kendall (1998), Dominated cftp was introduced in order to handle unbounded state spaces. The idea is to introduce a Markov chain (Dt) coupled to our Markov chain (Xt), such that Xt ≤ Dt for all ... |

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Citation Context ...ng in finite time. In fact, for fixed U and V , (1 + x)U ̸= (1 + x ′ )U when x ̸= x ′ whereas the range of x ↦→ f(x, U, V ) is discrete. For the algorithm we describe, f acts as a multigamma coupler (=-=Murdoch and Green, 1998-=-) f ′ (x, u, v) = u(x + 1)1u(x+1)≥1 + v1u(x+1)<1. The reason we mention f instead of f ′ is that f has more chances of coalescence than f ′ . Even though this is not explicitly used by the algorithm w... |

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