BMGL-EV.RdDensity, distribution function, and h-function the bivariate MGL-EV and survival MGL-EV copula with copula parameter delta.
pcMGLEV.bivar(u1, u2, param)
dcMGLEV.bivar(u1, u2, param)
pcMGLEV180.bivar(u1, u2, param)
dcMGLEV180.bivar(u1, u2, param)
hcMGLEV180.bivar(u1, u2, param)
hcMGLEV.bivar(u1, u2, param)numeric vectors of equal length with values in \([0,1]\).
copula parameter, denoted by delta.
dcMGLEV.bivar, pcMGLEV.bivar and hMGLEV.bivar give values of density distribution and h-function for the 2-dimensional MGL copula with copula parameter \(\delta>0\).
dcMGLEV180.bivar, pcMGLEV180.bivar and hMGLEV180.bivar give values of density and distribution and h-function for the 2-dimensional MGL copula with copula parameter \(\delta>0\).
hMGLEV.bivar and hMGLEV180.bivar return 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.
pcMGLEV.bivar(u1 = c(0.3, 0.9), u2 = c(0.5, 0.8), param = 2)
#> [1] 0.2586206 0.7602469
dcMGLEV.bivar(u1 = 0.001, u2 = 0.999, param = 1)
#> [1] 0.01644683
pcMGLEV180.bivar(u1 = c(0.3, 0.9), u2 = c(0.5, 0.8), param = 2)
#> [1] 0.2492633 0.7813228
dcMGLEV180.bivar(u1 = 0.5, u2 = 0.78, param = 1.8)
#> [1] 0.9513845
hcMGLEV180.bivar(u1 = 0.5, u2 = 0.78, param = 1.8)
#> $hfunc1
#> [1] 0.8908632
#>
#> $hfunc2
#> [1] 0.2316631
#>
hcMGLEV.bivar(u1 = 0.5, u2 = 0.78, param = 1.8)
#> $hfunc1
#> [1] 0.8314307
#>
#> $hfunc2
#> [1] 0.2392104
#>