> 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
The cdf
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 Z3, Y4 < Inf) =
P(Y1 <
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