dcop {dsfa}

R Documentation

Copula function

Description

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

Usage

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

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

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

Arguments

W	numeric matrix of pseudo observations. Must have two columns.
delta	numeric vector of copula parameter \delta.
distr	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_2 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="normal")
cdf <- pcop(W=cbind(u,v), delta=p, distr="normal")
r <- rcop(n=100, delta=p, distr="normal")

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