# [SciPy-User] solving integration, density function

Tue Dec 21 06:48:27 CST 2010

```-------- Original-Nachricht --------
> Datum: Tue, 21 Dec 2010 13:20:47 +0100
> Von: Gregor Thalhammer <Gregor.Thalhammer@gmail.com>
> An: SciPy Users List <scipy-user@scipy.org>
> Betreff: Re: [SciPy-User] solving integration, density function

>
> Am 21.12.2010 um 12:06 schrieb Johannes Radinger:
>
> > Hello,
> >
> > I am really new to python and Scipy.
> > I want to solve a integrated function with a python script
> > and I think Scipy should do that :)
> >
> >
> > I do have some variables (s, m, K,) which are now absolutely set, but in
> future I'll get the values via another process of pyhton.
> >
> > s = 400
> > m = 0
> > K = 1
> >
> > And have have following function:
> > (1/((s*K)*sqrt(2*pi)))*exp((-1/2*(((x-m)/s*K))^2) which is the density
> function of the normal distribution a symetrical curve with the mean (m) of
> 0.
> >
> > The total area under the curve is 1 (100%) which is for an integration
> from -inf to +inf.
> > I want to know x in the case of 99%: meaning that the integral (-x to
> +x) of the function is 0.99. Due to the symetry of the curve you can also set
> the integral from 0 to +x equal to (0.99/2):
> >
> > 0.99 = integral((1/((s*K)*sqrt(2*pi)))*exp((-1/2*(((x-m)/s*K))^2)), -x,
> x)
> > resp.
> > (0.99/2) = integral((1/((s*K)*sqrt(2*pi)))*exp((-1/2*(((x-m)/s*K))^2)),
> 0, x)
> >
> > How can I solve that question in Scipy/python
> > so that I get x in the end. I don't know how to write
> > the code...
>
>
> --->
> erf(x[, out])
>
>     y=erf(z) returns the error function of complex argument defined as
>     as 2/sqrt(pi)*integral(exp(-t**2),t=0..z)
> ---
>
> from scipy.special import erf, erfinv
> erfinv(0.99)*sqrt(2)
>
>
> Gregor
>

Thank you Gregor,
I only understand a part of your answer... I know that the integral of the density function is a error function and I know that the argument "from scipy.special import erf, erfinv" is to load the module.

But how do I write the code including my orignial function so that I can modify it (I have also another function I want to integrate). how do i start? I want to save the whole code to a python-script I can then load e.g. into ArcGIS where I want to use the value of x for further calculations.

thanks

/johannes

> >
> > thank you very much
> >
> > johannes
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