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

 `1` ```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`

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.

`copreg`, `mle_marginal`
 `1` ```##---- This is an internal function called by copreg() ---- ```