| Library: | insurance |
| See also: | INSpremgam INSpremwei INSprempareto INSpremlogn INSpremburr |
| Quantlet: | INSapproxgamma | |
| Description: | returns the parameters for the translated gamma approximation of the compound Poisson distribution. |
| Usage: | {alpha, beta, x0} = INSapproxgamma (m1, m2, m3, lambda) | |
| Input: | ||
| m1 | scalar, first moment of the claim ditribution | |
| m2 | scalar, second (non-central) moment of the claim ditribution | |
| m3 | scalar, third (non-central) moment of the claim ditribution | |
| lambda | scalar, intensity of the Poisson arrival process | |
| Output: | ||
| alpha | scalar, alpha parameter of the translated gamma distribution | |
| beta | scalar, beta parameter of the translated gamma distribution | |
| x0 | scalar, x0 parameter of the translated gamma distribution | |
library("insurance")
library("distribs")
library("plot")
lambda = 25
expNbr = lambda
varNbr = lambda
logMu = 18.44
logSi = 1.1348
firstMoment = exp(logMu + 0.5*logSi^2)
secondMoment = exp(2*logMu+2*logSi^2)
thirdMoment = exp(3*logMu + 9*logSi^2/3)
param = INSapproxgamma(firstMoment, secondMoment, thirdMoment, lambda)
xaxis =(1:10)/100
p = INSpremgamma(param.alpha, param.beta, param.x0, xaxis, 5) / 1e9
plot(setmask(xaxis~p, "line", "red", "dashed"))
setgopt(plotdisplay,1,1,"yvalue",0|1)
setgopt(plotdisplay,1,1,"xvalue",0|1)
setgopt(plotdisplay,1,1,"xlabel","Quantile parameter epsilon","ylabel","Quantile premium(USD billion)")
Display showing the quantile-based premium for the translated gamma loss approximation of a lognormal distribution.