# 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

 `1` ```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`

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