BiCopDeriv2 | R Documentation |
This function evaluates the second derivative of a given parametric bivariate copula density with respect to its parameter(s) and/or its arguments.
BiCopDeriv2(
u1,
u2,
family,
par,
par2 = 0,
deriv = "par",
obj = NULL,
check.pars = TRUE
)
u1 , u2 |
numeric vectors of equal length with values in |
family |
integer; single number or vector of size |
par |
Copula parameter. |
par2 |
integer; single number or vector of size |
deriv |
Derivative argument |
obj |
|
check.pars |
logical; default is |
If the family and parameter specification is stored in a BiCop()
object obj
, the alternative version
BiCopDeriv2(u1, u2, obj, deriv = "par")
can be used.
A numeric vector of the second-order bivariate copula derivative
of the copula family
with parameter(s) par
, par2
with respect to deriv
evaluated at u1
and u2
.
Ulf Schepsmeier, Jakob Stoeber
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.
RVineGrad()
, RVineHessian()
,
BiCopDeriv()
, BiCopHfuncDeriv()
, BiCop()
## simulate from a bivariate Student-t copula
set.seed(123)
cop <- BiCop(family = 2, par = -0.7, par2 = 4)
simdata <- BiCopSim(100, cop)
## second derivative of the Student-t copula w.r.t. the first parameter
u1 <- simdata[,1]
u2 <- simdata[,2]
BiCopDeriv2(u1, u2, cop, deriv = "par")
## estimate a Student-t copula for the simulated data
cop <- BiCopEst(u1, u2, family = 2)
## and evaluate its second derivative w.r.t. the second argument u2
BiCopDeriv2(u1, u2, cop, deriv = "u2")
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