# st: Solved: approximation for binormal

 From "Robert Duval" To statalist@hsphsun2.harvard.edu Subject st: Solved: approximation for binormal Date Mon, 5 Feb 2007 19:01:56 -0500

```Dear all,

I think I solved my own previous posting.

If the problem of using 1-binormal(a,b;rho) as an approximation for
1-Pr(x>a,y>b;rho)  is created by cancellation error (when
binormal(a,b;rho) is close to 1), then the former quantity can be
approximated by

binormal(-a,b,-rho) + binormal(a,-b,-rho) + binormal(-a,-b,rho)

Since this only involves additions of small terms it shouldn't face
the same accuracy problems.

robert

On 2/5/07, Robert Duval <rduval@gmail.com> wrote:
```
```Sorry there was a typo in my previous posting... here is the correct one

On 2/5/07, Robert Duval <rduval@gmail.com> wrote:
> Dear friends
>
> In the ml book (Gould, Pitblado and Sribney)  it is mentioned that
>
> 1-normal(a) is a poor numerical approximation for Pr(x>a) and instead
> they suggest using
>
> normal(-a).
>
> Does anyone knows of a similar expression for the bivariate normal
> case giving 1-Pr(x>a,y>b;rho) without using
>
> 1-binormal(a,b;rho)
>
> i.e. without using substractions (or additions) that make the
> approximation numerically poor.?
>
> Any help would be greatly appreciated.
>
> Robert
> *
>
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```
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```