Class "moCopula" of Marshall-Olkin Copulas
The Marshall-Olkin copula class.
The (2-dimensional) "MO" copula with parameter theta in [0,1]^2 is (i.e., its CDF is)
C(u1, u2) = min(u1 * u2^(1 - theta2), u1^(1 - theta1) * u2).
Consequently, the density is undefined on a curve (in [0,1]^2), namely for the points u=(u1,u2) where two expressions in the above min(f(u), g(u)) are equal, f(u)=g(u). It is easy to see that that is equivalent to
u1^theta_1 = u2^theta2.
Objects can be created by new("moCopula", ...) but are
typically produced by moCopula(...).
dimension:Numeric (scalar), the dimension of the copula.
exprdist:a length two expression with
expressions for the CDF and PDF of the copula.
parameters:numeric vector of two parameter values in [0,1].
param.names:"character" vector of length two.
param.lowbnd:numeric vector of two values in [0,1].
param.upbnd:numeric vector of two values in [0,1].
fullname:(deprecated; do not use!)
Typical copula methods work, see "moCopula"
and use methods(class = "moCopula").
Class "moCopula" extends class "copula" directly.
Nelsen, R. B. (2006), An introduction to Copulas, Springer, New York.
moCopula for constructing them;
copula-class.
moCopula()@exprdist[["cdf"]] # a simple definition
methods(class = "moCopula")
contourplot2(moCopula(c(.1, .8)), pCopula, main= "moCopula((0.1, 0.8))")
Xmo <- rCopula(5000, moCopula(c(.2, .5)))
try( # gives an error, as there is no density (!):
loglikCopula(c(.1, .2), Xmo, moCopula())
)
plot(moCopula(c(.9, .2)), n = 10000, xaxs="i", yaxs="i",
# opaque color (for "density effect"):
pch = 16, col = adjustcolor("black", 0.3))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.