mle_marginal: ML-estimates of the marginal models

In CopulaRegression: Bivariate Copula Based Regression Models

Description

We fit the Gamma and the (zero-truncated) Poisson model separately.

Usage

mle_marginal(x, y, R, S, family,exposure,sd.error=FALSE,zt=TRUE)

Arguments

x	n observations of the Gamma variable
y	n observations of the (zero-truncated) Poisson variable
R	n x p design matrix for the Gamma model
S	n x q design matrix for the zero-truncated Poisson model
family	an integer defining the bivariate copula family: 1 = Gauss, 3 = Clayton, 4=Gumbel, 5=Frank
exposure	exposure time for the zero-truncated Poisson model, all entries of the vector have to be >0. Default is a constant vector of 1.
sd.error	logical. Should the standard errors of the regression coefficients be returned? Default is FALSE.
zt	logical. If zt=TRUE, we use a zero-truncated Poisson variable. Otherwise, we use a Poisson variable. Default is TRUE.

Details

This is an internal function called by copreg.

Value

alpha	estimated coefficients for X, including the intercept
beta	estimated coefficients for Y, including the intercept
sd.alpha	estimated standard deviation (if sd.error=TRUE)
sd.beta	estimated standard deviation (if sd.error=TRUE)
delta	estimated dispersion parameter
theta	0, in combination with family=1, this corresponds to the independence assumption
family	1, in combination with theta=0, this corresponds to the independence assumption
family0	copula family as provided in the function call
theta.ifm	estimated copula parameter, estimated via inference from margins
tau.ifm	estimated value of Kendall's tau, estimated via inference from margins
ll	loglikelihood of the estimated model, assuming independence,evaluated at each observation
loglik	overall loglikelihood, assuming independence, i.e. sum of ll
ll.ifm	loglikelihood of the estimated model, using theta.ifm as the copula parameter, evaluated at each observation
loglik.ifm	overall loglikelihood, using theta.ifm as the copula parameter, i.e. sum of ll.ifm

Author(s)

Nicole Kraemer

References

N. Kraemer, E. Brechmann, D. Silvestrini, C. Czado (2013): Total loss estimation using copula-based regression models. Insurance: Mathematics and Economics 53 (3), 829 - 839.

See Also

copreg, mle_joint

Examples

##---- This is an internal function called by copreg() ----

CopulaRegression documentation built on May 29, 2017, 5:47 p.m.