hBMGL: Conditional Distribution Function of a Bivariate MGL and...

In lizhengxiao/rMGLReg: MGL copula regressions

Description

Conditional Distribution Function of a Bivariate MGL and survival Copula

Usage

hcMGL.bivar(u1, u2, pars)

hcMGL180.bivar(u1, u2, pars)

Arguments

u1	numeric vectors of equal length with values in [0,1].
u2	numeric vectors of equal length with values in [0,1].
pars	numeric; single number or vector of size length(u1); copula parameter > 0.

Details

The h-function is defined as the conditional distribution function of a bivariate copula, i.e.,

h_1(u_2|u_1,δ) := P(U_2 ≤q u_2 | U_1 = u_1) = \partial C(u_1,u_2) / \partial u_1,

h_2(u_1|u_2,δ) := P(U_1 ≤q 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) δ. For more details see Aas et al. (2009).

Value

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,

References

Zhengxiao Li, Jan Beirlant, Liang Yang. A new class of copula regression models for modelling multivariate heavy-tailed data. 2021, arXiv:2108.05511.

Examples

hcMGL.bivar(u1 = c(0.1, 0.001, 0.3), u2 = c(0, 0.9999, 0.88), pars = 2)
hcMGL180.bivar(u1 = c(0.1, 0.001, 0.3), u2 = c(0, 0.9999, 0.88), pars = 2)

lizhengxiao/rMGLReg documentation built on Jan. 2, 2022, 8:52 a.m.