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# Verteilungsfunktion für die eindimensionale Randdichte f(xn) einer Truncated Multivariate Normal Distribution,
# vgl. Jack Cartinhour (1990) "One-dimensional marginal density functions of a truncated multivariate normal density function" für die Dichtefunktion
#
# @param xn Vektor der Länge l von Punkten, an dem die Verteilungsfunktion ausgewertet wird
# @param i Index (1..n) dessen Randdichte berechnet werden soll
# @param mean (nx1) Mittelwertvektor
# @param sigma (nxn)-Kovarianzmatrix
# @param lower,upper Trunkierungsvektor lower <= x <= upper
ptmvnorm.marginal <- function(xn, n=1, mean=rep(0, nrow(sigma)), sigma=diag(length(mean)), lower=rep(-Inf, length = length(mean)), upper=rep( Inf, length = length(mean)))
{
# check of standard tmvnorm arguments
cargs <- checkTmvArgs(mean, sigma, lower, upper)
mean <- cargs$mean
sigma <- cargs$sigma
lower <- cargs$lower
upper <- cargs$upper
if (n < 1 || n > length(mean) || !is.numeric(n) || length(n) > 1 || !n %in% 1:length(mean))
{
stop("n must be a integer scalar in 1..length(mean)")
}
# Anzahl der Dimensionen
k = length(mean)
Fx = numeric(length(xn))
upper2 = upper
alpha = pmvnorm(lower = lower, upper = upper, mean = mean, sigma = sigma)
for (i in 1:length(xn))
{
upper2[n] = xn[i]
Fx[i] = pmvnorm(lower=lower, upper=upper2, mean=mean, sigma=sigma)
}
return (Fx/alpha)
}
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