Sampling Exponentially Tilted Stable Distributions
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];
see the references for more details about this distribution.
retstable(alpha, V0, h = 1, method = NULL) retstableR(alpha, V0, h = 1)
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). |
method |
a character string denoting the method to use, currently
either |
retstableR is a pure R version of "MH", however, not as fast as
retstable (implemented in C, based on both methods) and therefore not
recommended in simulations when run time matters.
A vector of variates from tS(alpha, 1, .....); see above.
Devroye, L. (2009) Random variate generation for exponentially and polynomially tilted stable distributions, ACM Transactions on Modeling and Computer Simulation 19, 18, 1–20.
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.
rstable1 for sampling stable distributions.
## 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))
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