Revision **161411bb86f97e5a8bd89091cd61d03a33c2761a** authored by Martin Maechler on **06 February 2012, 00:00:00 UTC**, committed by Gabor Csardi on **06 February 2012, 00:00:00 UTC**

Tip revision: **161411bb86f97e5a8bd89091cd61d03a33c2761a** authored by ** Martin Maechler ** on **06 February 2012, 00:00:00 UTC**

**version 0.8-0**

Tip revision: **161411b**

retstable.Rd

```
\name{retstable}
\alias{retstable}
\alias{retstableR}
\title{Sampling Exponentially Tilted Stable Distributions}
\description{
Generating random variates of an exponentially tilted stable
distribution of the form
\deqn{\tilde{S}(\alpha, 1, (\cos(\alpha\pi/2)V_0)^{1/\alpha},
V_0\mathbf{1}_{\{\alpha=1\}}, h\mathbf{1}_{\{\alpha\ne 1\}}; 1),
}{tS(alpha, 1, (cos(alpha*pi/2)V0)^(1/alpha), V0*1_(alpha==1), h*1_(alpha!=1)),}
with parameters
\eqn{\alpha\in(0,1]}{alpha in (0,1]}, \eqn{V_0\in(0,\infty)}{V0 in (0,Inf)},
and \eqn{h\in[0,\infty)}{h in [0,Inf)} and corresponding Laplace-Stieltjes transform
\deqn{\exp(-V_0((h+t)^\alpha-h^\alpha)),\ t\in[0,\infty];
}{exp(-V0((h+t)^alpha-h^alpha)), t in [0,Inf];}
see the references for more details about this distribution.
}
\usage{
retstable(alpha, V0, h = 1, method = NULL)
retstableR(alpha, V0, h = 1)
}
\arguments{
\item{alpha}{parameter in \eqn{(0,1]}.}
\item{V0}{vector of values in \eqn{(0,\infty)}{(0,Inf)} (for example, when
sampling nested Clayton copulas, these are random variates from
\eqn{F_0}{F0}), that is, the distribution corresponding to
\eqn{\psi_0}{psi0}.}
\item{h}{parameter in \eqn{[0,\infty)}{[0,Inf)}.}
\item{method}{a character string denoting the method to use, currently
either \code{"MH"} (Marius Hofert's algorithm) or \code{"LD"} (Luc Devroye's
algorithm). By default, when \code{NULL}, a smart choice is made to use the
fastest of these methods depending on the specific values of \eqn{V_0}{V0}.}
}
\details{
\code{retstableR} is a pure \R version of \code{"MH"}, however, not as fast as
\code{retstable} (implemented in C, based on both methods) and therefore not
recommended in simulations when run time matters.
}
\value{
A vector of variates from \eqn{\tilde{S}(\alpha, 1, .....)}{tS(alpha, 1, .....)}; see above.
}
\author{Marius Hofert, Martin Maechler}
\seealso{
\code{\link{rstable1}} for sampling stable distributions.
}
\references{
Hofert, M. (2011)
Efficiently sampling nested Archimedean copulas,
\emph{Computational Statistics & Data Analysis} \bold{55}, 57--70.
Hofert, M. (2012),
Sampling exponentially tilted stable distributions,
\emph{ACM Transactions on Modeling and Computer Simulation} \bold{22}, 1,
page numbers: to be announced.
}
\examples{
## Draw random variates from an exponentially tilted stable distribution
## with given alpha, V0, and h = 1
alpha <- .2
V0 <- rgamma(200, 1)
rETS <- retstable(alpha, V0)
## Distribution plot the random variates -- log-scaled
hist(log(rETS), prob=TRUE)
lines(density(log(rETS)), col=2)
rug (log(rETS))
}
\keyword{distribution}
```

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