Re: Integrating a normal distribution many times

[Quentin Spencer]

Søren Hauberg wrote:
> Hi,
>    This is not necessarily an Octave question. but here goes anyway.
>    I need to evaluate the integrate a normal distribution over a 
> specific interval with many mean values. My current Octave 
> implementation just calls 'quad' at mean value, i.e.
>
> for t = linspace(0, 32, 750)
>    qq = @(x) normal_pdf(x, t, 2.5);
>    result = quad(qq, 19, 26, 0)
> endfor
>
> This is, however, fairly slow. At some point my system needs to run in 
> real-time (not in an Octave implementation), so I doubt that the above 
> strategy will work. Does anybody have some hints on how to speed this 
> up? Should I precalculate a lookup table with some values and then 
> interpolate when I need to evaluate the function at a new mean value?
>   

The best way to make this faster in octave is to use the error function 
("erf" in octave). Any integral of the normal probability density 
function can be expressed in terms of the error function. If you 
eventually need this in C, I don't know whether math.h includes erf or 
not, but you might look at how octave is computing it.


Quentin