CLcop {copBasic} | R Documentation |
The Clayton Copula
Description
The Clayton copula (Joe, 2014, p. 168) is
where . The copula, as
limits, to the countermonotonicity coupla (
;
W
), as limits to the independence copula (
;
P
), and as , limits to the comonotonicity copula (
;
M
). The parameter is readily computed from a Kendall Tau (
tauCOP
) by .
Usage
CLcop(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
# Lower tail dependency of Theta = pi --> 2^(-1/pi) = 0.8020089 (Joe, 2014, p. 168)
taildepCOP(cop=CLcop, para=pi)$lambdaL # 0.80201