{
#function to calulate the CDF of a vector..
#Estimate the CDF at N points on a grid
#Suppose 'x' is the vector containing the data

#Example create data from Normal distribution..

x = rnorm(500)

#create a bunch of points to estimate the CDF
N=250
xx1=seq(min(x),max(x),length=N)
xx=c(-999,xx1)

source("qgaus.r")

#source the function you wish to use for integration
# Normal, Gamma, Lognormal etc..
source("integrand-normal.r")
#source("integrand-gamma.r")


# CDF at  the created points 'xxl' using numerical integration
zz=1:N
N1=N+1
 for(i in 2:N1){
x1=xx[i-1]
 x2=xx[i]
 zz[i-1]=qgaus(x1,x2,x)}
zz=cumsum(zz)

# CDF at the points 'xxl' using the CDF command - i.e., 'pnorm'
zz1=pnorm(xx1,mean(x),sd(x))

# Plot the CDf from the numerical integratrion..
plot(xxl, zz, xlab="X', ylab="CDF, F(x)", type="l", col="red")

#overlay CDF from the 'pnorm' command
lines(xxl, zzl, col="blue")

#if we want to estimate the CDF at the data points
#xs=sort(x)
#N=length(x)
#zz=1:N
#for(i in 1:N){
#zz[i]=qgaus(-999,xs[i],x)}
#zz1=pnorm(xs,mean(x),sd(x))

#get a quantile..
#xp=runif(1,0,1)
#zzx=c(xp,zz)
#zord=rank(zzx)
#qp=xs[zord[1]]
#qnorm(xp,mean(x),sd(x))


}