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.

Other copula: cop(), delta_bounds()
u=0.3; v=0.7; p=0.5