#
#   funcs.R - A set of R functions for studying aggregation of
#                      correlated risk porfolios
#
#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.
#
#



disc.metodo.round <- structure(c(0.000473987103245853, 0.0416050327111922, 0.164080831467209,
0.237857591737151, 0.217607182758463, 0.153672065363593, 0.0920072871791147,
0.0491406283685871, 0.0241391989622163, 0.0111238468505793, 0.00487424011845172, 
0.00205053290516322, 0.000834116178070943, 0.000329863091219518,
0.000127353872015123, 4.81622719928909e-05, 1.78888558766133e-05,
6.5401976485635e-06, 2.35787098945561e-06, 8.39517884765328e-07,
2.95582440745790e-07), .Names = c("0", "500", "1000", "1500",
"2000", "2500", "3000", "3500", "4000", "4500", "5000", "5500",
"6000", "6500", "7000", "7500", "8000", "8500", "9000", "9500",
"10000"))


gamma.discretizada <- function(x,f) {
vals <- as.numeric(names(f))
resposta <- numeric(length(x))
	for (i in seq(along=x)) {
		resposta[i] <- sum(f[vals <= x[i]])
	}
resposta
}

metodo.match <- function() {
	j <- 1:20
	h <- 500
	resposta <- numeric(length(j)+1)
	resposta[1] <- 1 - integrate(pgamma,0,h,lower.tail=FALSE,shape=5,rate=1/400)$value/h

	for (i in 2:length(j)) {
		resposta[i] <- (2*integrate(pgamma,0,h*j[i-1],lower.tail=FALSE,shape=5,rate=1/400)$value - integrate(pgamma,0,h*(j[i-1]-1),lower.tail=FALSE,shape=5,rate=1/400)$value - integrate(pgamma,0,h*(j[i-1]+1),lower.tail=FALSE,shape=5,rate=1/400)$value)/h
	}
	names(resposta) <- c(0,j*h)
	resposta
}