R help - Feb 2009 - Normal cdf modified function

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

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
> 
> ______________________________________________
> R-help at 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.

> 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, and some elementary algebra, is enough to compute the
probability you are interested in.
> two types of inequalities ("<" and ">") can be
mixed? (The user would
> have to specify the set of indexes with inequalities of the type
">")
Giovanni

-- 

Giovanni Petris  <GPetris at uark.edu>
Associate Professor
Department of Mathematical Sciences
University of Arkansas - Fayetteville, AR 72701
Ph: (479) 575-6324, 575-8630 (fax)
http://definetti.uark.edu/~gpetris/