[SciPy-User] solving integration, density function

[Johannes Radinger]

Thank you for the simplification of the formula,
but I still get a different result in the case
when x<s1 (eg. x=2, s1=3).

here a code to try:

********************
import math
from scipy import stats

s1 = 3
m = 0
p = 1
x = 2

func = stats.norm.pdf(x, loc=m, scale=(s1))
func2 = (1/(s1*math.sqrt(2*math.pi)) * math.exp(-0.5*((x-m)/s1)**2))

print func
print func2
********************************

/j

-------- Original-Nachricht --------
> Datum: Thu, 6 Jan 2011 05:48:25 -0600
> Von: Warren Weckesser <warren.weckesser at enthought.com>
> An: SciPy Users List <scipy-user at scipy.org>
> Betreff: Re: [SciPy-User] solving integration, density function

> 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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