Expectation of the policy loss

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Description

Expectation and variance of the policy loss

Usage

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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

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

dpolicy_loss

Examples

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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)