itdr.new {Runuran} | R Documentation |
UNU.RAN random variate generator for continuous distributions with given probability density function (PDF). It is based on the Inverse Transformed Density Rejection method (‘ITDR’).
[Universal] – Rejection Method.
itdr.new(pdf, dpdf, lb, ub, pole, islog=FALSE, ...)
pdf |
probability density function. (R function) |
dpdf |
derivative of pdf . (R function) |
pole |
pole of distribution. (numeric) |
lb |
lower bound of domain;
use -Inf if unbounded from left. (numeric) |
ub |
upper bound of domain;
use Inf if unbounded from right. (numeric) |
islog |
whether pdf is given as log-density (the
dpdf must then be the derivative of the
log-density). (boolean) |
... |
(optional) arguments for pdf |
This function creates a unuran
object based on “ITDR”
(Inverse Transformed Density Rejection). It can be used to draw samples of a
continuous random variate with given probability density function
using ur
.
The density must be provided by a function pdf
which must
return non-negative numbers and which need not be normalized (i.e., it
can be any multiple of a density function).
Moreover, it must be monotone on its domain.
The algorithm is especially designed for distributions with unbounded
densities. Thus the algorithm need the position of the pole
.
The derivative dpdf
is essential. (Numerical derivation does
not work as it results in serious round-off errors.)
The setup time of this method depends on the given PDF, whereas its marginal generation times are almost independent of the target distribution.
Josef Leydold and Wolfgang H"ormann unuran@statmath.wu-wien.ac.at.
W. H"ormann, J. Leydold, and G. Derflinger (2007): Inverse transformed density rejection for unbounded monotone densities. ACM Trans. Model. Comput. Simul. 17(4), Article 18, 16 pages. DOI = 10.1145/1276927.1276931
ur
, unuran.new
, unuran
.
## Create a sample of size 100 for a Gamma(-0.5) distribution pdf <- function (x) { x^(-0.5)*exp(-x) } dpdf <- function (x) { (-x^(-0.5) - 0.5*x^(-1.5))*exp(-x) } gen <- itdr.new(pdf=pdf, dpdf=dpdf, lb=0, ub=Inf, pole=0) x <- ur(gen,100)