CopulaRegression (version 0.1-5)

mle_joint: ML-Estimates of the joint model.

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.

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 $g(\theta)$ (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

Details

This is an internal function called by copreg.

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() ----