mle_joint: ML-Estimates of the joint model.

In CopulaRegression: Bivariate Copula Based Regression Models

Description

Computes the maximum-likelihood estimates for the regression coefficients and the copula parameter.

Usage

mle_joint(alpha0,beta0,theta0, delta0, x, y, R, S, family, exposure, sd.error,zt)

Arguments

alpha0	The starting value of the regression coefficients for the Gamma regression
beta0	The starting value of the regression coefficients for the (zero-truncated) Poisson regression
theta0	The starting value of the copula parameter
delta0	The starting value for the dispersion parameter of the Gamma distribution
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)
sd.g.theta	estimated standard deviation of g(θ) (if sd.error=TRUE)
delta	estimated dispersion parameter
theta	estimated copula parameter
tau	estimated value of Kendall's tau
family	copula family
ll	loglikelihood of the estimated model, evaluated at each observation
loglik	overall loglikelihood, i.e. sum of ll

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_marginal

Examples

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

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