[SciPy-User] solving integration, density function

[Warren Weckesser]

On Thu, Jan 6, 2011 at 5:27 AM, Johannes Radinger <JRadinger at gmx.at> wrote:

> Hey
>
> Last time you helped me a lot with my normal
> probabilty density function. My problem now is
> quite simple, I think it's just a problem with
> the syntax (brackets):
>
> There are two ways to calculate the pdf, with the
> stats-function and with pure mathematically, but
> the give different results and I can't find the
> where I make the mistake:
>
>
> func1 = stats.norm.pdf(x, loc=m, scale=(s1))
> func2 =
> 1/((s1)*(math.sqrt(2*math.pi))))*(math.exp(((-0.5)*((x-m)/(s1)))**2)
>
> Where is the problem
>


func2 = 1/(s1*math.sqrt(2*math.pi)) * math.exp(-0.5*((x-m)/s1)**2)


Warren



> thank you...
>
> /j
>
> -------- Original-Nachricht --------
> > Datum: Tue, 21 Dec 2010 09:18:15 -0500
> > Von: Skipper Seabold <jsseabold at gmail.com>
> > An: SciPy Users List <scipy-user at scipy.org>
> > Betreff: Re: [SciPy-User] solving integration, density function
>
> > On Tue, Dec 21, 2010 at 7:48 AM, Johannes Radinger <JRadinger at gmx.at>
> > wrote:
> > >
> > > -------- Original-Nachricht --------
> > >> Datum: Tue, 21 Dec 2010 13:20:47 +0100
> > >> Von: Gregor Thalhammer <Gregor.Thalhammer at gmail.com>
> > >> An: SciPy Users List <scipy-user at 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 :)
> > >> >
> > >> > My task:
> > >> >
> > >> > 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.
> > >
> >
> > Are you always integrating densities?  If so, you don't want to use
> > integrals probably, but you could use scipy.stats
> >
> > erfinv(.99)*np.sqrt(2)
> > 2.5758293035489004
> >
> > from scipy import stats
> >
> > stats.norm.ppf(.995)
> > 2.5758293035489004
> >
> > Skipper
> > _______________________________________________
> > SciPy-User mailing list
> > SciPy-User at scipy.org
> > http://mail.scipy.org/mailman/listinfo/scipy-user
>
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