JOcopB5 {copBasic} | R Documentation |
The Joe/B5 Copula (B5)
Description
The Joe/B5 copula (Joe, 2014, p. 170) is
where .
The copula as
limits to the comonotonicity coupla (
and
M
), as limits to independence copula (
;
P
). Finally, the parameter is readily computed from a Kendall Tau (
tauCOP
) by
where is the
digamma()
function and as then
where is the
trigamma()
function.
Usage
JOcopB5(u, v, para=NULL, tau=NULL, ...)
Arguments
u |
Nonexceedance probability |
v |
Nonexceedance probability |
para |
A vector (single element) of parameters—the |
tau |
Optional Kendall Tau; and |
... |
Additional arguments to pass. |
Value
Value(s) for the copula are returned. Otherwise if tau
is given, then the is computed and a
list
having
para |
The parameter |
tau |
Kendall Tau. |
and if para=NULL
and tau=NULL
, then the values within u
and v
are used to compute Kendall Tau and then compute the parameter, and these are returned in the aforementioned list.
Author(s)
W.H. Asquith
References
Joe, H., 2014, Dependence modeling with copulas: Boca Raton, CRC Press, 462 p.
See Also
Examples
# Upper tail dependency of Theta = pi --> 2 - 2^(1/pi) = 0.753131 (Joe, 2014, p. 171).
taildepCOP(cop=JOcopB5, para=pi)$lambdaU # 0.75313
# Blomqvist Beta of Theta = pi (Joe, 2014, p. 171).
blomCOP(cop=JOcopB5, para=pi) # 0.5521328
3 - 4*(2*(1/2)^pi - (1/4)^pi)^(1/pi) # 0.5521328
## Not run:
# A test near the limiting Theta for trigamma()
UV <- simCOP(cop=JOcopB5, para=2, n=10000)
para <- JOcopB5(UV[,1], UV[,2])$para
message("Tau difference ", round(2-para, digits=2), " is small.") #
## End(Not run)