math-fun {copula} | R Documentation |
sinc(x)
computes the sinc function
s(x) = sin(x)/x for x != 0 and
s(0) = 1, such that s() is continuous, also at x = 0.
A..Z(x, a)
computes Zolotarev's function to
the power 1-a
.
sinc(x) A..Z(x, alpha, I.alpha = 1 - alpha)
x |
|
alpha |
parameter in (0,1]. |
I.alpha |
must be |
For more details about Zolotarev's function, see, for example, Devroye (2009).
A..Z(x,alpha)
is A~Z(x,alpha),
defined as
sin(alpha*x)^alpha * sin((1-alpha)*x)^(1-alpha) / sin(x), x in [0,pi],
where alpha in (0,1] is alpha
.
Martin Maechler
Devroye, L. (2009) Random variate generation for exponentially and polynomially tilted stable distributions, ACM Transactions on Modeling and Computer Simulation 19, 18, 1–20.
retstable
internally makes use of these functions.
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")