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.