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.