dcop {dsfa}

R Documentation

Copula function

Description

Probablitiy density function, distribution and random number generation for copulas.

Usage

dcop(
  W,
  delta,
  distr_cop = "normal",
  rot = 0,
  deriv_order = 0,
  tri = NULL,
  log.p = FALSE
)

pcop(W, delta = 0, distr_cop = "normal", rot = 0, log.p = FALSE)

rcop(n, delta = 0, distr_cop = "normal", rot = 0)

Arguments

W	numeric matrix of pseudo observations. Must have two columns.
delta	numeric vector of copula parameter \delta.
distr_cop	string, defines the copula family: independent = Independence copula normal = Gaussian copula clayton = Clayton copula gumbel = Gumbel copula frank = Frank copula joe = Joe copula amh = Ali-Mikhail-Haq copula
rot	integer determining the rotation for Archimedian copulas. Can be 90, 180 or 270.
deriv_order	integer; maximum order of derivative. Available are 0,2 and 4.
tri	optional; index matrix for upper triangular, generated by trind_generator().
log.p	logical; if TRUE, probabilities p are given as log(p).
n	positive integer; number of observations.

Details

A two-dimensional copula C(w_1, w_2, \delta) is a multivariate cumulative distribution function for which the marginal probability distribution of w_1 and w_1 are uniform on the interval [0,1]. The parameter \delta specifies the copula.

The functions pcop() and rcop() are wrapper functions for the pCopula() and rCopula().

Value

dcop gives the density, pcop gives the distribution function for a specified copula and rcop generates random numbers, with given delta. dcop() returns a derivs object. For more details see trind() and trind_generator().

Functions

• pcop(): distribution function for copula.

• rcop(): random number generation for copula.

References

• Schepsmeier U, Stöber J (2014). “Derivatives and Fisher information of bivariate copulas.” Statistical Papers, 55(2), 525–542.

• Hofert M, Kojadinovic I, Mächler M, Yan J (2018). Elements of copula modeling with R. Springer.

See Also

Other copula: cop(), delta_bounds()

Examples

u=0.3; v=0.7; p=0.5
pdf <- dcop(W=cbind(u,v), delta=p, distr_cop="normal")
cdf <- pcop(W=cbind(u,v), delta=p, distr_cop="normal")
r <- rcop(n=100, delta=p, distr_cop="normal")

---