math-fun | R Documentation |
sinc(x)
computes the sinc function
s(x)=\sin(x)/x
for x\ne 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 \tilde A_{Z}(x,\alpha)
,
defined as
\frac{\sin(\alpha x)^\alpha\sin((1-\alpha)x)^{1-\alpha}}{\sin(x)},\
x\in[0,\pi],
where \alpha\in(0,1]
is alpha
.
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")
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