P {copBasic} | R Documentation |
The Product (Independence) Copula
Description
Compute the product copula (Nelsen, 2006, p. 12), which is defined as
This is the copula of statistical independence between and
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]