R: Class "moCopula" of Marshall-Olkin Copulas

moCopula-class {copula} | R Documentation

## Class "moCopula" of Marshall-Olkin Copulas

### Description

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 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))

[Package copula version 1.0-1 Index]