hBMGL.RdConditional Distribution Function of a Bivariate MGL and survival Copula
hcMGL.bivar(u1, u2, pars)
hcMGL180.bivar(u1, u2, pars)numeric vectors of equal length with values in \([0,1]\).
numeric vectors of equal length with values in \([0,1]\).
numeric; single number or vector of size length(u1); copula parameter > 0.
hcMGL.bivar/hcMGL180.bivar returns a list with
hfunc1: \(\partial C(u_1,u_2) / \partial u_1,\)
hfunc2: \(\partial C(u_1,u_2) / \partial u_2,\)
The h-function is defined as the conditional distribution function of a bivariate copula, i.e., $$h_1(u_2|u_1,\delta) := P(U_2 \leq u_2 | U_1 = u_1) = \partial C(u_1,u_2) / \partial u_1,$$
$$h_2(u_1|u_2,\delta) := P(U_1 \leq u_1 | U_2 = u_2) := \partial C(u_1,u_2) / \partial u_2,$$
where \((U_1, U_2) \sim C\), and \(C\) is a bivariate copula distribution function with parameter(s) \(\delta\). For more details see Aas et al. (2009).
Zhengxiao Li, Jan Beirlant, Liang Yang. A new class of copula regression models for modelling multivariate heavy-tailed data. 2021, arXiv:2108.05511.
hcMGL.bivar(u1 = c(0.1, 0.001, 0.3), u2 = c(0, 0.9999, 0.88), pars = 2)
#> $hfunc1
#> [1] 0.0000000 0.9999998 0.9137196
#>
#> $hfunc2
#> [1] 0.9999900000 0.0000012337 0.1123161318
#>
hcMGL180.bivar(u1 = c(0.1, 0.001, 0.3), u2 = c(0, 0.9999, 0.88), pars = 2)
#> $hfunc1
#> [1] 0.0000000 1.0000000 0.9778406
#>
#> $hfunc2
#> [1] 1.564345e-01 2.467403e-07 9.504334e-02
#>