Quantile of the policy loss

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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) 

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