# dpolicy_loss: Density of the policy loss In CopulaRegression: Bivariate Copula Based Regression Models

## Description

Density of the policy loss

## Usage

 1 dpolicy_loss(l, mu, delta, lambda, theta, family, y.max = 300,zt=TRUE) 

## Arguments

 l vector at which the density is evaluated mu expectation of the Gamma distribution delta dispersion parameter of the Gamma distribution lambda parameter of the (zero-truncated) Poisson distribution theta copula parameter family an integer defining the bivariate copula family: 1 = Gauss, 3 = Clayton, 4=Gumbel, 5=Frank y.max upper value of the finite sum that we use to approximate the infinite sum, see below for details zt logical. If zt=TRUE, we use a zero-truncated Poisson variable. Otherwise, we use a Poisson variable. Default is TRUE.

## Details

For a Gamma distributed variable X and a (zero truncated) Possion variable Y, the policy loss is defined as L=X\cdot Y. Its density is an infinite sum of weighted Gamma densities. The parameter y.max is the upper value of the finite sum that approximates the infinite sum.

## Value

density, evaluated at the vector l

## Note

lambda and mu can be scalars, or vectors of the same length as l

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.

epolicy_loss, qpolicy_loss
  1 2 3 4 5 6 7 8 9 10 # example taken from the paper library(VineCopula) mu<-1000 delta<-0.09 lambda<-2.5 family<-1 theta<-BiCopTau2Par(tau=0.5,family=family) l<-seq(1,7000,length=100) out<-dpolicy_loss(l,mu,delta,lambda,theta,family) plot(l,out,type="l",lwd=3,xlab="loss",ylab="density")