>>>>> As a closed-form expression.
>>
>> Right. So what you're actually saying is that you can't compute the 
>> confidence interval exactly using a finite number of applications of a 
>> particular arbitrarily chosen set of functions - the elementary 
>> functions.
> 
> That is indeed the definition.
> 
> This obviously doesn't matter for scott's case since he just wants a 
> numeric answer and Excel seems to have erf built in, I just wanted to 
> point out that far from being "relatively easy" to work out, the 
> cumulative distribution function of a Gaussian is generally the first 
> function people encounter which is impossible to actually compute in 
> closed form (normally this will come up in first or second year calculus 
> at some point).  I'll agree that at first glance it certainly *looks* 
> like it would be simple to compute though, which is part of why it's 
> interesting.

Well, the sine and cosine functions can't be computed by a finite number 
of additions, subtractions, multiplications, divisions and exponents. 
But since sine and cosine are included in the arbitrary "set of 
permissible functions", they don't count. But erf is not, so it does count.

To me, it seems that approximating erf (or its inverse) is no harder 
than approximating a sine or cosine - and we do that all day.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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