Inverse Conditional Distribution Function of a Bivariate Copula
Evaluate the inverse conditional distribution function (inverse h-function) of a given parametric bivariate copula.
BiCopHinv(u1, u2, family, par, par2 = 0, obj = NULL, check.pars = TRUE) BiCopHinv1(u1, u2, family, par, par2 = 0, obj = NULL, check.pars = TRUE) BiCopHinv2(u1, u2, family, par, par2 = 0, obj = NULL, check.pars = TRUE)
u1, u2 |
numeric vectors of equal length with values in [0,1]. |
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,θ) := P(U_2 ≤ u_2 | U_1 = u_1) = \partial C(u_1,u_2) / \partial u_1,
h_2(u_1|u_2,θ) := P(U_1 ≤ u_1 | U_2 = u_2) := \partial C(u_1,u_2) / \partial u_2,
where (U_1, U_2) \sim C, and C is a bivariate copula distribution
function with parameter(s) θ.
For more details see Aas et al. (2009).
If the family and parameter specification is stored in a BiCop()
object obj, the alternative version
BiCopHinv(u1, u2, obj), BiCopHinv1(u1, u2, obj), BiCopHinv2(u1, u2, obj)
can be used.
BiCopHinv returns a list with
hinv1 |
Numeric vector of the inverse conditional distribution function
(inverse h-function) of the copula |
hinv2 |
Numeric vector of the inverse conditional distribution function
(inverse h-function) of the copula |
BiCopHinv1 is a faster version that only calculates hinv1;
BiCopHinv2 only calculates hinv2.
Ulf Schepsmeier, Thomas Nagler
Aas, K., C. Czado, A. Frigessi, and H. Bakken (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44 (2), 182-198.
# inverse h-functions of the Gaussian copula cop <- BiCop(1, 0.5) hi <- BiCopHinv(0.1, 0.2, cop) # or using the fast versions hi1 <- BiCopHinv1(0.1, 0.2, cop) hi2 <- BiCopHinv2(0.1, 0.2, cop) all.equal(hi$hinv1, hi1) all.equal(hi$hinv2, hi2) # check if it is actually the inverse cop <- BiCop(3, 3) all.equal(0.2, BiCopHfunc1(0.1, BiCopHinv1(0.1, 0.2, cop), cop)) all.equal(0.1, BiCopHfunc2(BiCopHinv2(0.1, 0.2, cop), 0.2, cop))
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