P {copBasic} | R Documentation |
The Product (Independence) Copula
Description
Compute the product copula (Nelsen, 2006, p. 12), which is defined as
\mathbf{\Pi}(u,v) = uv\mbox{.}
This is the copula of statistical independence between U
and V
and is sometimes referred to as the independence copula. The two extreme antithesis copulas are the Fréchet–Hoeffding upper-bound (M
) and Fréchet–Hoeffding lower-bound (W
) copulas.
Usage
P(u, v, ...)
Arguments
u |
Nonexceedance probability |
v |
Nonexceedance probability |
... |
Additional arguments to pass. |
Value
Value(s) for the copula are returned.
Author(s)
W.H. Asquith
References
Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.
See Also
Examples
P(c(0.4, 0, 1), c(0, 0.6, 1))
## Not run:
n <- 100000 # giant sample size, L-comoments are zero
# PERFECT INDEPENDENCE
UV <- simCOP(n=n, cop=P, graphics=FALSE)
lmomco::lcomoms2(UV, nmom=4)
# The following are Taus_r^{12} and Taus_r^{21}
# L-corr: 0.00265 and 0.00264 ---> ZERO
# L-coskew: -0.00121 and 0.00359 ---> ZERO
# L-cokurtosis: 0.00123 and 0.00262 ---> ZERO
# MODEST POSITIVE CORRELATION
rho <- 0.6; # Spearman Rho
theta <- PLACKETTpar(rho=rho) # Theta = 5.115658
UV <- simCOP(n=n, cop=PLACKETTcop, para=theta, graphics=FALSE)
lmomco::lcomoms2(UV, nmom=4)
# The following are Taus_r^{12} and Taus_r^{21}
# L-corr 0.50136 and 0.50138 ---> Pearson R == Spearman Rho
# L-coskews -0.00641 and -0.00347 ---> ZERO
# L-cokurtosis -0.00153 and 0.00046 ---> ZERO
## End(Not run)
[Package copBasic version 2.2.4 Index]