moCopula-class | R Documentation |
The Marshall-Olkin copula class.
The (2-dimensional) "MO" copula with parameter
\bold\theta\in [0,1]^2
is (i.e., its CDF is)
C(u_1, u_2) = min(u_1 * u_2^(1 - \theta_2), u_1^(1 - \theta_1) * u_2).%
Consequently, the density is undefined on a curve (in [0,1]^2
),
namely for the points \bold{u}=(u_1,u_2)
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
u_1^{\theta_1} = u_2^{\theta_2}.
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))
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