#
#   simula_panjer.R - A set of R functions for studying Panjer 
#                      aggregation method
#
#Copyright (C) 2005 Fernando Henrique F. P. Rosa <academic at feferraz.net>
#
# 
#This program is free software; you can redistribute it and/or
#modify it under the terms of version 2 of the GNU General Public License
#as published by the Free Software Foundation.  A copy of this license should
#be included in the file COPYING.
#
#This program is distributed in the hope that it will be useful,
#but WITHOUT ANY WARRANTY; without even the implied warranty of
#MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#GNU General Public License for more details.
#
#You should have received a copy of the GNU General Public License
#along with this program; if not, write to the Free Software
#Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
#
#

simula <- function(N) {
        sn.obs <- function(x) {
                sum(sample(1:4,size=x,prob=c(1/8,1/4,1/4,3/8),replace=T))
        }

	tam <- rpois(N,2)
	obs <- sapply(tam,sn.obs)
	obs

}


calcula.g <- function(R) {
	f <- function(k) { 
		dist <- numeric(4)
		dist[1] <- 1/8
		dist[2] <- 1/4
		dist[3] <- 1/4
		dist[4] <- 3/8
		if (k < 5 & k > 0) {
			dist[k]
		}
		else {
			0
		}
	}

	g <- numeric(R+1)

	g[0+1] <- exp(-2)
	b <- 2

	for (r in 1:R) {
		for (i in 1:r) {
			g[r+1] <- g[r+1] + (b*(i/r) * f(i)*g[r-i+1])
		}
	}

	g

}