>>>>>> I presume it's relatively easy to work out the inverse function 
>>>>>> for a normal distribution...
>>>>>
>>>>> Actually it's impossible to analytically compute.
>>>>
>>>> Define "analytically".
>>>
>>> As a closed-form expression.  As I said, it's still possible to 
>>> compute numerically.
>>
>> And Sqrt[2] erf^-1 (2z - 1) doesn't count because...?
> 
> erf isn't an elementary function.  See:
> 
> http://en.wikipedia.org/wiki/Closed-form_expression
> 
> http://en.wikipedia.org/wiki/Error_function#Taylor_series

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.

Post a reply to this message