# Roughly estimating parameters for an assumed distribution
# Apr.27,2004, by Minato NAKAZAWA
# Sample size should be set as N
N <- 1000
# Data should be set as x
# here, parameters 1 and 2 are in fact unknown
x <- rweibull(N,1,2)
# Calculating cumulative distribution
cx <- qqplot(x,1:N/N,plot=F)
# Obtaining the shape parameter as a, the scale parameter as b
# by nonlinear regression. User must state start by intuition.
nls(y ~ pweibull(x,a,b), data=cx, start=list(a=0.5,b=1.5))
# Alternatively, function optim() can be used, but the result was worse.
# fr <- function(x) { (cx$y-pweibull(cx$x,x[1],x[2]))^2 }
# optim(c(0.5,1.5),fr)