moCopula-class {copula}

Class "moCopula" of Marshall-Olkin Copulas

Description

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 from the Class

Objects can be created by new("moCopula", ...) but are typically produced by moCopula(...).

Slots

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!)

Methods

Typical copula methods work, see "moCopula" and use methods(class = "moCopula").

Extends

Class "moCopula" extends class "copula" directly.

References

Nelsen, R. B. (2006), An introduction to Copulas, Springer, New York.

See Also

moCopula for constructing them; copula-class.

Examples

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))