[SciPy-User] How to fit a curve/function?

[Johannes Radinger]

-------- Original-Nachricht --------
> Datum: Wed, 8 Jun 2011 07:10:38 -0400
> Von: josef.pktd at gmail.com
> An: SciPy Users List <scipy-user at scipy.org>
> Betreff: Re: [SciPy-User] How to fit a curve/function?

> On Wed, Jun 8, 2011 at 6:52 AM, Johannes Radinger <JRadinger at gmx.at>
> wrote:
> > Hello,
> >
> > I've got following function describing any kind of animal dispersal
> kernel:
> >
> > def pdf(x,s1,s2):
> >    return
> (p/(math.sqrt(2*math.pi*s1**2))*numpy.exp(-((x-0)**(2)/(2*s1**(2)))))+((1-p)/(s2*math.sqrt(2*math.pi))*numpy.exp(-((x-0)**(2)/(2*s2**(2)))))
> >
> > On the other hand I've got data from literature with which I want to fit
> the function so that I get s1, s2 and x.
> > Ususally the data in the literature are as follows:
> >
> > Example 1: 50% of the animals are between -270m and +270m and 90%  are
> between -500m and + 500m
> >
> > Example 2: 84% is between - 5000 m and +5000m, and 73% are between
> -1000m and +1000m
> >
> > So far as I understand an integration of the function is needed to solve
> for s1 and s2 as all the literature data give percentage (area under the
> curve) Can that be used to fit the curve or can that create ranges for s1
> and s2.
> 
> I don't see a way around integration.
> 
> If you have exactly 2 probabilities, then you can you a solver like
> scipy.optimize.fsolve to match the probabilites
> eg.
> 0.5 = integral pdf from -270 to 270
> 0.9 = integral pdf from -500 to 500
> 
> If you have more than 2 probabilities, then using optimization of a
> weighted function of the moment conditions would be better.
> 
> Josef



Hello again

I tried following, but without success so far. What do I have to do excactly...

import numpy
from scipy import stats
from scipy import integrate
from scipy.optimize import fsolve
import math

p=0.3

def pdf(x,s1,s2):
    return (p/(math.sqrt(2*math.pi*s1**2))*numpy.exp(-((x-0)**(2)/(2*s1**(2)))))+((1-p)/(s2*math.sqrt(2*math.pi))*numpy.exp(-((x-0)**(2)/(2*s2**(2)))))

def equ(s1,s2):
    0.5==integrate.quad(pdf,-270,270,args=(s1,s2))
    0.9==integrate.quad(pdf,-500,500,args=(s1,s2))

result=fsolve(equ, 1,500)

print result


/Johannes
> 
> >
> > /Johannes
> >
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