MomentsApprox: Aggregate distribution approximation based on moments

In lucazama/CollectiveRisk: Collective Risk Model Functions.

Description

Function to approximate the Cumulative Distribution Function (CDF) of the aggregate claim size distribution.

Usage

MomentsApprox(m,moments,type,n)

Arguments

m	probability to approximate: P(S>m)
moments	vector of raw moments of the aggregate distribution S. Besides the "Normal" approximation, all other
type	the available approximation methods are c("Normal","Gamma", "NormalPower", "NormalToGamma","GramCharlier", "Bowers")
n	approximation order, only needed for GramCharlier and Bowers c(3,4,5).
approximations	require at least the first 3 raw moments of S. "GramCharlier" and "Bowers" require as many raw moments as their chosen approximation order.

Details

The function takes as input the first raw moments of the aggregate claim size distribution S and returns the desired approximation to P(S>m) based on moments. The available approximations are c("Normal","Gamma", "NormalPower", "NormalToGamma","GramCharlier", "Bowers"). For GramCharlier and Bowers, the approximations are available up to the 5th order (n=c(3,4,5))

Examples

MomentsApprox(900,moments=AggregateRawMoments(Moments("Poisson",30,"raw"),Moments("Gamma",c(40,2),"raw")), "Bowers",n=3)
MomentsApprox(900,moments=AggregateRawMoments(Moments("Poisson",30,"raw"),Moments("Gamma",c(40,2),"raw")), "NormalToGamma")

lucazama/CollectiveRisk documentation built on July 25, 2020, 7:22 a.m.