CopulaRegression (version 0.1-4)

mle_marginal: ML-estimates of the marginal models

Description

We fit the Gamma and the (zero-truncated) Poisson model separately.

Usage

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.

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

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_joint

Examples

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