VineCopula: BiCopDeriv – R documentation

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BiCopDeriv

Derivatives of a Bivariate Copula Density

Description

This function evaluates the derivative of a given parametric bivariate copula density with respect to its parameter(s) or one of its arguments.

Usage

BiCopDeriv(
  u1,
  u2,
  family,
  par,
  par2 = 0,
  deriv = "par",
  log = FALSE,
  obj = NULL,
  check.pars = TRUE
)

Arguments

`u1, u2`	numeric vectors of equal length with values in [0,1].
`family`	integer; single number or vector of size `length(u1)`; defines the bivariate copula family: `0` = independence copula `1` = Gaussian copula `2` = Student t copula (t-copula) `3` = Clayton copula `4` = Gumbel copula `5` = Frank copula `6` = Joe copula `13` = rotated Clayton copula (180 degrees; survival Clayton'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel”) `16` = rotated Joe copula (180 degrees; “survival Joe”) `23` = rotated Clayton copula (90 degrees) '24' = rotated Gumbel copula (90 degrees) '26' = rotated Joe copula (90 degrees) '33' = rotated Clayton copula (270 degrees) '34' = rotated Gumbel copula (270 degrees) '36' = rotated Joe copula (270 degrees)
`par`	numeric; single number or vector of size `length(u1)`; copula parameter.
`par2`	integer; single number or vector of size `length(u1)`; second parameter for the t-Copula; default is `par2 = 0`, should be an positive integer for the Students's t copula `family = 2`.
`deriv`	Derivative argument `"par"` = derivative with respect to the first parameter (default) `"par2"` = derivative with respect to the second parameter (only available for the t-copula) `"u1"` = derivative with respect to the first argument `u1` `"u2"` = derivative with respect to the second argument `u2`
`log`	Logical; if `TRUE` than the derivative of the log-likelihood is returned (default: `log = FALSE`; only available for the derivatives with respect to the parameter(s) (`deriv = "par"` or `deriv = "par2"`)).
`obj`	`BiCop` object containing the family and parameter specification.
`check.pars`	logical; default is `TRUE`; if `FALSE`, checks for family/parameter-consistency are omitted (should only be used with care).

Details

If the family and parameter specification is stored in a BiCop() object obj, the alternative version

BiCopDeriv(u1, u2, obj, deriv = "par", log = FALSE)

can be used.

Value

A numeric vector of the bivariate copula derivative

of the copula family
with parameter(s) par, par2
with respect to deriv,
evaluated at u1 and u2.

Author(s)

Ulf Schepsmeier

References

Schepsmeier, U. and J. Stoeber (2014). Derivatives and Fisher information of bivariate copulas. Statistical Papers, 55 (2), 525-542.
https://link.springer.com/article/10.1007/s00362-013-0498-x.

Examples

## simulate from a bivariate Student-t copula
set.seed(123)
cop <- BiCop(family = 2, par = -0.7, par2 = 4)
simdata <- BiCopSim(100, cop)

## derivative of the bivariate t-copula with respect to the first parameter
u1 <- simdata[,1]
u2 <- simdata[,2]
BiCopDeriv(u1, u2, cop, deriv = "par")

## estimate a Student-t copula for the simulated data
cop <- BiCopEst(u1, u2, family = 2)
## and evaluate its derivative w.r.t. the second argument u2
BiCopDeriv(u1, u2, cop, deriv = "u2")

VineCopula

Statistical Inference of Vine Copulas

v2.4.1

GPL (>= 2)

Authors

Thomas Nagler [aut, cre], Ulf Schepsmeier [aut], Jakob Stoeber [aut], Eike Christian Brechmann [aut], Benedikt Graeler [aut], Tobias Erhardt [aut], Carlos Almeida [ctb], Aleksey Min [ctb, ths], Claudia Czado [ctb, ths], Mathias Hofmann [ctb], Matthias Killiches [ctb], Harry Joe [ctb], Thibault Vatter [ctb]

Initial release