# qpolicy_loss: Quantile of the policy loss In CopulaRegression: Bivariate Copula Based Regression Models

## Description

Quantile of the policy loss

## Usage

 1 qpolicy_loss(q, mu, delta, lambda, theta, family, y.max = 20,zt=TRUE) 

## Arguments

 q value at which the quantile function 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 in the density, see below for more 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

quantile, evaluated at q

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.

## See Also

ppolicy_loss,epolicy_loss,dpolicy_loss

## Examples

 1 2 3 4 5 6 7 8 library(VineCopula) mu<-1000 delta<-0.09 lambda<-2.5 family<-1 theta<-BiCopTau2Par(tau=0.5,family=family) # upper quartile out<-qpolicy_loss(0.75,mu,delta,lambda,theta,family) 

CopulaRegression documentation built on May 29, 2017, 5:47 p.m.