MGL.mle.mixed: Fitting bivariate MGL copula models for mixed data
In lizhengxiao/rMGLReg: MGL copula regressions

Description Usage Arguments Details Value Examples

MGL.mle.mixed is used to fit bivariate mixed copula regression models via maximum likelihood (ML) method for continuous and semi-continuous variables.

MGL.mle.mixed(
  obs,
  U,
  U_,
  f,
  copula = c("MGL", "MGL180", "MGL-EV", "MGL-EV180", "Gumbel", "Normal", "MGB2", "t"),
  umin,
  hessian = TRUE,
  initpar,
  ...
)

`obs`	two-dimensional matrix for loss observations (y1, y2).
`U`	two-dimenstional matrix for pseudo copula data with values in [0,1] for (F(y1), F(y2)).
`U_`	two-dimensional matrix for pseudo copula data for the data (F(y1), F(y2-1)).
`f`	values of the density function for marginal distribution.
`copula`	copula 'MGL', 'MGL180', "MGL-EV", "MGL-EV180", "MGB2", "Normal" , "t".
`umin`	threshold value used in the semi-continuous data.
`hessian`	Logical. Should a numerically differentiated Hessian matrix be returned?
`initpar`	Initial values for the parameters to be optimized over.
`...`	additional arguments, see `nlm` for more details.

The estimation method is performed via nlm function. Y1: continuous variable Y2: semi-continuous variable when Y2>umin, it is continuous and Y2<=umin is discrete.

For a portfolio of n observations (y_{i1},y_{i2}; \; i=1,…,n), the joint density function of (Y_1,Y_2) can be written as

f_{Y_{1},Y_2}(y_{i1},y_{i2})=\begin{cases} f_{Y_1}(y_{i1})[ h_{2|1}(F_{Y_{1}}(y_{i1}),F_{Y_{2}}(y_{i2})) - h_{2|1}(F_{Y_{1}}(y_{i1}),F_{Y_{2}}(y_{i2}-1)) ], & y_{i2}≤ umin,\\ f_{Y_1}(y_{i1})f_{Y_2}(y_{i2})c(F_{Y_{1}}(y_{i1}), F_{Y_{2}}(y_{i2})), & y_{i2} > umin, \end{cases}

where the density f_{Y_j}(\cdot) and cdf F_{Y_j}(\cdot) of the marginal distributions (i=1,2) are specified respectively. Here h_{2|1}(u_1, u_2)=\partial C(u_1,u_2)/\partial u_1 is the h-function of bivariate copula.

copula:

"MGB2" is multivariate GB2.
"Normal" and "t" denote the Gaussian copula and Student-t copula respectively.
"MGL" and "MGL-EV" denote the MGL and MGL-EV copula respectively.
"MGL180" and "MGL-EV180" denote the survival MGL and survival MGL-EV copula respectively.
"Gumbel" is Gumbel copula.#'

A list containing the following components:

loglike: the value of the estimated maximum of the loglikelihood function.
copula: the name of the fitted copula. "MGL180" and "MGL-EV180" denote the survival MGL and MGL-EV copula respectively.
estimates: the point at which the maximum value of the loglikelihood is obtained.
se: the standard errors of the estimators.
AIC, BIC: the goodness fit of the regression models.
hessian: the hessian at the estimated maximum of the loglikelihood (if requested).

library(rMGLReg)
# load the Chinese earthquake data set
u <- cbind(earthqCHI$u1, earthqCHI$u2) # cdf of marginal distribution
u_ <- cbind(earthqCHI$u1, earthqCHI$u2_) # cdf of marginal distribution for Y1 and Y2 - 1
y <- cbind(earthqCHI$y1, earthqCHI$y2)  # observations
f <- cbind(earthqCHI$f1, earthqCHI$f2) # pdf of marginal distribution
obs <- y
U <- u
U_ <- u_
umin <- 20
m.MGLMGA180 <- MGL.mle.mixed(obs = y, U = U, U_ = U_,
umin = umin, f = f,
copula = "MGL180",
method = "L-BFGS-B", initpar = c(2))
m.MGLMGA180