BMGL-EV: Bivarite MGL-EV and survival MGL-EV copula

In lizhengxiao/rMGLReg: MGL copula regressions

Description

Density, distribution function, and h-function the bivariate MGL-EV and survival MGL-EV copula with copula parameter delta.

Usage

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)

Arguments

u1, u2	numeric vectors of equal length with values in [0,1].
param	copula parameter, denoted by delta.

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

• dcMGLEV.bivar, pcMGLEV.bivar and hMGLEV.bivar give values of density distribution and h-function for the 2-dimensional MGL copula with copula parameter δ>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 δ>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,

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

pcMGLEV.bivar(u1 = c(0.3, 0.9), u2 = c(0.5, 0.8), param = 2)
dcMGLEV.bivar(u1 = 0.001, u2 = 0.999, param = 1)
pcMGLEV180.bivar(u1 = c(0.3, 0.9), u2 = c(0.5, 0.8), param = 2)
dcMGLEV180.bivar(u1 = 0.5, u2 = 0.78, param = 1.8)
hcMGLEV180.bivar(u1 = 0.5, u2 = 0.78, param = 1.8)
hcMGLEV.bivar(u1 = 0.5, u2 = 0.78, param = 1.8)

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