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Normal cdf modified function

David Winsemius

Wed, Feb 18, 2009 5:55 AM

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 <fsaldan1 at 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
> 
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