R help - Nov 2005 - normal cdf over an interval

Hi, 

I'm trying to find a way to take evaluate the Normal CDF over an interval
and return the result on the log scale.  This works, but I think it isn't
numerically stable:

log(pnorm(a, mean = x, sd = y) - pnorm(b, mean = x, sd = y))

Does anyone know of a single function that does the above?  Or knows of a way to
make it more stable?  I'd really appreciate any suggestions!

Thanks, 

Olivia
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On 16-Nov-05 Olivia Lau wrote:
> Hi, 
> 
> I'm trying to find a way to take evaluate the Normal CDF over an
> interval and return the result on the log scale.  This works, but I
> think it isn't numerically stable:  
> 
> log(pnorm(a, mean = x, sd = y) - pnorm(b, mean = x, sd = y))
> 
> Does anyone know of a single function that does the above?  Or knows of
> a way to make it more stable?  I'd really appreciate any suggestions!  
> 
> Thanks, 
> 
> Olivia
A little more detail might be helpful.

Your formula is simple enough in itself, and you should not be
getting numerical stability problems for reasonable values of
(a-x)/y or (b-x)/y (say in the range -4 to 4). And I assume
you're being careful that a > b!

So for what values of your variables are problems arising?
And how do they manifest themselves?

If it's due to large values of (a-x)/y etc., then possibly
an asymptotic approximation may serve. There are some good
ones around.

Can you tell us a bit more?

Best wishes,
Ted.


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Date: 16-Nov-05                                       Time: 20:37:47
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