itdr.new: UNU.RAN generator based on Inverse Transformed Density...
In Runuran: R Interface to the 'UNU.RAN' Random Variate Generators

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 2	itdr.new(pdf, dpdf, lb, ub, pole, islog=FALSE, ...) itdrd.new(distr)

`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`.
`distr`	distribution object. (S4 object of class `"unuran.cont"`)

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 pdf must be positive but need not be normalized (i.e., it can be any multiple of a density function). The algorithm is especially designed for distributions with unbounded densities. Thus the algorithm needs the position of the pole. Moreover, the given function must be monotone on its domain.

The derivative dpdf is essential. (Numerical derivation does not work as it results in serious round-off errors.)

Alternatively, one can use function itdrd.new where the object distr of class "unuran.cont" must contain all required information about the distribution.

The setup time of this method depends on the given PDF, whereas its marginal generation times are almost independent of the target distribution.

An object of class "unuran".

Josef Leydold and Wolfgang H\"ormann [email protected].

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.cont, 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)

## Alternative approach
distr <- udgamma(shape=0.5)
gen <- itdrd.new(distr)
x <- ur(gen,100)