# retstable: Sampling exponentially tilted stable distributions In BayesBridge: Bridge Regression

## Description

From the copula package:

Generating random variates of an exponentially tilted stable distribution of the form

tS(alpha, 1, (cos(alpha*pi/2)V0)^(1/alpha), V0*1_(alpha==1), h*1_(alpha!=1)),

with parameters alpha in (0,1], V0 in (0,Inf), and h in [0,Inf) and corresponding Laplace-Stieltjes transform

exp(-V0((h+t)^alpha-h^alpha)), t in [0,Inf];

## Usage

 `1` ```retstable.ld(num=1, alpha=1, V0=1, h=1) ```

## Arguments

 `num` Number of random variates to generate `alpha` parameter in (0,1]. `V0` vector of values in (0,Inf) (for example, when sampling nested Clayton copulas, these are random variates from F0), that is, the distribution corresponding to psi0. `h` parameter in [0,Inf).

## Value

A vector of variates from tS(alpha, 1, .....); see above.

## Author(s)

Marius Hofert, Martin Maechler

## References

Hofert, M. (2011) Efficiently sampling nested Archimedean copulas, Computational Statistics & Data Analysis 55, 57–70.

Hofert, M. (2012), Sampling exponentially tilted stable distributions, ACM Transactions on Modeling and Computer Simulation 22, 1, page numbers: to be announced.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## Draw random variates from an exponentially tilted stable distribution ## with given alpha, V0, and h = 1 alpha <- .2 N = 200 V0 <- rgamma(N, 1) rETS <- retstable.ld(N, alpha, V0) ## Distribution plot the random variates -- log-scaled hist(log(rETS), prob=TRUE) lines(density(log(rETS)), col=2) rug (log(rETS)) ```

BayesBridge documentation built on May 29, 2017, 10:40 a.m.