rDickman {SubTS}

Simulation from the generalized Dickman distribution

Description

Simulates from the generalized Dickman distribution using Algorithm 3.1 in Dassios, Qu, and Lim (2019).

Usage

rDickman(n, t, b = 1)

Arguments

n

Number of observations.

t

Parameter > 0.

b

Parameter > 0.

Details

Simulates from the generalized Dickman distribution by using Algorithm 3.1 in Dassios, Qu, and Lim (2019). This distribution has Laplace transform

L(z) = exp( t int_0^b (e^(-xz)-1) x^(-1) dx), z>0

and Levy measure

M(dx) = t x^(-1) 1(0<x<b) dx.

When b=1 and t=1, this is the Dickman distribution.

Value

Returns a vector of n random numbers.

Author(s)

Michael Grabchak and Lijuan Cao

References

A. Dassios, Y. Qu, J.W. Lim (2019). Exact simulation of generalised Vervaat perpetuities. Journal of Applied Probability, 56(1):57-75.

M. Penrose and A. Wade (2004). Random minimal directed spanning trees and Dickman-type distributions. Advances in Applied Probability, 36(3):691-714.

Examples

rDickman(10, 1)