BiCopHfunc | R Documentation |
Evaluate the conditional distribution function (h-function) of a given parametric bivariate copula.
BiCopHfunc(u1, u2, family, par, par2 = 0, obj = NULL, check.pars = TRUE)
BiCopHfunc1(u1, u2, family, par, par2 = 0, obj = NULL, check.pars = TRUE)
BiCopHfunc2(u1, u2, family, par, par2 = 0, obj = NULL, check.pars = TRUE)
u1 , u2 |
numeric vectors of equal length with values in |
family |
integer; single number or vector of size |
par |
numeric; single number or vector of size |
par2 |
numeric; single number or vector of size |
obj |
|
check.pars |
logical; default is |
The h-function is defined as the conditional distribution function of a bivariate copula, i.e.,
h_1(u_2|u_1;\boldsymbol{\theta}) := P(U_2 \le u_2 | U_1 = u_1)
= \frac{\partial C(u_1, u_2; \boldsymbol{\theta})}{\partial u_1},
h_2(u_1|u_2;\boldsymbol{\theta}) := P(U_1 \le u_1 | U_2 = u_2)
= \frac{\partial C(u_1, u_2; \boldsymbol{\theta})}{\partial u_2},
where (U_1, U_2) \sim C
, and C
is a bivariate copula distribution
function with parameter(s) \boldsymbol{\theta}
.
For more details see Aas et al. (2009).
If the family and parameter specification is stored in a BiCop()
object obj
, the alternative versions
BiCopHfunc(u1, u2, obj) BiCopHfunc1(u1, u2, obj) BiCopHfunc2(u1, u2, obj)
can be used.
BiCopHfunc
returns a list with
hfunc1 |
Numeric vector of the conditional distribution
function (h-function) of the copula |
hfunc2 |
Numeric vector of the conditional distribution function
(h-function) of the copula |
BiCopHfunc1
is a faster version that only calculates hfunc1
;
BiCopHfunc2
only calculates hfunc2
.
Ulf Schepsmeier
Aas, K., C. Czado, A. Frigessi, and H. Bakken (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44 (2), 182-198.
BiCopHinv()
, BiCopPDF()
, BiCopCDF()
,
RVineLogLik()
, RVineSeqEst()
, BiCop()
data(daxreturns)
# h-functions of the Gaussian copula
cop <- BiCop(family = 1, par = 0.5)
h <- BiCopHfunc(daxreturns[, 2], daxreturns[, 1], cop)
# or using the fast versions
h1 <- BiCopHfunc1(daxreturns[, 2], daxreturns[, 1], cop)
h2 <- BiCopHfunc2(daxreturns[, 2], daxreturns[, 1], cop)
all.equal(h$hfunc1, h1)
all.equal(h$hfunc2, h2)
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