I would think this could be approached by segmenting the probability "volume" using identities such as these:
P(Y1 < Z1, Y2 < Z2, Y3 > Z3, Y4 > Z4) + P(Y1 < Z1, Y2 < Z2, Y3 > Z3, Y4 < Z4) = P(Y1 < Z1, Y2 < Z2, Y3 > Z3, Y4 < Inf) and P(Y1 < Z1, Y2 < Z2, Y3 < Z3, Y4 <Inf) + P(Y1 < Z1, Y2 < Z2, Y3 > Z3, Y4 < Inf) = P(Y1 < Z1, Y2 < Z2, Y3 <Inf, Y4 < Inf) -- David Winsemius Apologies for what will probably be an html formatted message -------------- Original message ---------------------- From: Fernando Saldanha <fsald...@gmail.com> > I wonder if an R package would have a function that calculates the following. > > Let Y be a normal multivariate function. For example, let Y have 4 > dimensions. I want to calculate > > P(Y1 < Z1, Y2 < Z2, Y3 > Z3, Y4 > Z4). > > There are R functions to do the calculation if all the inequalities > are of the type "<" (the cdf). But is there an R function where the > two types of inequalities ("<" and ">") can be mixed? (The user would > have to specify the set of indexes with inequalities of the type ">") > > Thanks for any suggestions. > > FS > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.