math-fun {copula} | R Documentation |
Sinc, Zolotarev's, and Other Mathematical Utility Functions
Description
sinc(x)
computes the sinc function
for
and
, such that
is continuous, also at
.
A..Z(x, a)
computes Zolotarev's function to
the power 1-a
.
Usage
sinc(x)
A..Z(x, alpha, I.alpha = 1 - alpha)
Arguments
x |
|
alpha |
parameter in (0,1]. |
I.alpha |
must be |
Details
For more details about Zolotarev's function, see, for example, Devroye (2009).
Value
A..Z(x,alpha)
is ,
defined as
where is
alpha
.
References
Devroye, L. (2009) Random variate generation for exponentially and polynomially tilted stable distributions, ACM Transactions on Modeling and Computer Simulation 19, 18, 1–20.
See Also
retstable
internally makes use of these functions.
Examples
curve(sinc, -15,25); abline(h=0,v=0, lty=2)
curve(A..Z(x, 0.25), xlim = c(-4,4),
main = "Zolotarev's function A(x) ^ 1-alpha")
[Package copula version 1.1-3 Index]