Density of the policy loss

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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

Author(s)

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

epolicy_loss, qpolicy_loss

Examples

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# 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")