# epolicy_loss: Expectation of the policy loss

Description Usage Arguments Details Value Author(s) References See Also Examples

### Description

Expectation and variance of the policy loss

### Usage

 1 epolicy_loss(mu, delta, lambda, theta, family, y.max = 300,zt=TRUE,compute.var=FALSE) 

### Arguments

 mu expectation of the Gamma distribution, can be a vector delta dispersion parameter of the Gamma distribution lambda parameter of the (zero-truncated) Poisson distribution, can be a vector of the same length as mu 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 in the density, 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. compute.var logical. If compute.var=TRUE, we also compute the variance of the policy loss. Default is FALSE.

### 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

 mean expectation of the policy loss var variance of the policy loss

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.

dpolicy_loss

### Examples

 1 2 3 4 5 6 7 library(VineCopula) mu<-1000 delta<-0.09 lambda<-2.5 family<-3 theta<-BiCopTau2Par(tau=0.5,family=family) out<-epolicy_loss(mu,delta,lambda,theta,family) 

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