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# program: spuRs/resources/scripts/ppoint.r
phi <- function(x) return(exp(-x^2/2)/sqrt(2*pi))
ppoint <- function(p, pdf = phi, z.min = -10, tol = 1e-9) {
# calculate a percentage point
#
# p is assumed to be between 0 and 1
# pdf is assumed to be a probability density function
#
# let F(x) be the integral of pdf from -infinity to x
# we apply the Newton-Raphson algorithm to find z_p such that
# F(z_p) = p, that is, to find z_p such that F(z_p) - p = 0
# note that the derivative of F(z) - p is just pdf(z)
#
# we approximate -infinity by z.min (that is, we assume that
# the integral of pdf from -infinity to z.min is negligible)
# do first iteration
x <- 0
f.x <- simpson_n(pdf, z.min, x) - p
# continue iterating until stopping conditions are met
while (abs(f.x) > tol) {
x <- x - f.x/pdf(x)
f.x <- simpson_n(pdf, z.min, x) - p
}
return(x)
}
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