[SciPy-User] how to fit a given pdf

Benjamin Root ben.root@ou....
Wed Aug 11 13:29:36 CDT 2010


On Wed, Aug 11, 2010 at 1:15 PM, <josef.pktd@gmail.com> wrote:

> On Wed, Aug 11, 2010 at 1:48 PM, Benjamin Root <ben.root@ou.edu> wrote:
> > On Wed, Aug 11, 2010 at 11:14 AM, Jonathan Stickel <jjstickel@vcn.com>
> > wrote:
> >>
> >> On 8/11/10 09:00 , scipy-user-request@scipy.org wrote:
> >> > Date: Wed, 11 Aug 2010 12:00:22 -0300
> >> > From: Renato Fabbri<renato.fabbri@gmail.com>
> >> > Subject: [SciPy-User] how to fit a given pdf
> >> > To: Discussion of Numerical Python<numpy-discussion@scipy.org>,
> >> >       scipy-user@scipy.org
> >> > Message-ID:
> >> >       <AANLkTinmmEbSo9_-ZmCXDzqDXLZb1fM8zFVoM-gnHo+c@mail.gmail.com<AANLkTinmmEbSo9_-ZmCXDzqDXLZb1fM8zFVoM-gnHo%2Bc@mail.gmail.com>
> >
> >> > Content-Type: text/plain; charset="iso-8859-1"
> >> >
> >> > Dear All,
> >> >
> >> > help appreciated, thanks in advance.
> >> >
> >> > how do you fit a pdf you have with a given pdf (say gamma).
> >> >
> >> > with the file attached, you can go like:
> >> >
> >> > a=open("AC-010_ED-1m37F100P0.txt","rb")
> >> > aa=a.read()
> >> > aaa=aa[1:-1].split(",")
> >> > data=[int(i) for i in aaa]
> >> >
> >> > if you do pylab.plot(data); pylab.show()
> >> >
> >> > The data is something like:
> >> > ___|\___
> >> >
> >> > It is my pdf (probability density function).
> >> >
> >> > how can i find the right parameters to make that fit with a gamma?
> >> >
> >> > if i was looking for a normal pdf, for example, i would just find mean
> >> > and std and ask for the pdf.
> >> >
> >> > i've been playing with scipy.stats.distributions.gamma but i have not
> >> > reached anything.
> >> >
> >> > we can extend the discussion further, but this is a good starting
> point.
> >> >
> >> > any idea?
> >> >
> >>
> >> I am not familiar with the scipy.stats module, and so I do not know what
> >> it can do for you.  However, I would just generate a model gamma
> >> distribution from the mean and variance, just as for a normal
> >> distribution.  The gamma distribution equation can be written as
> >>
> >> p(x) = p0/(b^a*Gamma(a))*x^(a-1)*exp(-x/b)
> >>
> >> assuming x starts at zero (x>=0)
> >> (http://en.wikipedia.org/wiki/Gamma_distribution).  Then the the
> >> parameters a and b are related to the mean and variance by
> >>
> >> a = mean^2/var
> >> b = var/mean
> >>
> >> (I did the algebra quickly just now, and so you might want to
> >> double-check).  p0 is the area under the distribution and may be simply
> >> 1 if your distribution is normalized.
> >>
> >> Hope this helps.
> >>
> >> Jonathan
> >
> > Note, those are the point estimators for gamma distribution, but it does
> not
> > use maximum likeihood estimation (MLE).  Using MLE, finding the estimator
> > for alpha is tricky, requiring convergence.  Probably best to use the fit
> > module as Josef mentioned.  However, there is a decent estimator for the
> > estimator (I heard you liked estimation...)
> >
> > a = 0.5 / (ln(mean(X)) - mean(ln(X)))
> >
> > Note that if you have a zero value in your dataset this won't work.
> Also,
> > the reference is not 100% clear if it is a base 10 log or not.  I am
> pretty
> > certain it is a natural log.
>
> Travis also added a different estimator in
>
> http://projects.scipy.org/scipy/browser/trunk/scipy/stats/distributions.py#L2867
> I never looked specifically at gamma, only as example for generic MLE,
> and have no idea what this estimator is.
>
> Ben, do you have the reference or know what type of estimators your's is?
>
> (I like references, the R package POT has 17 estimators for genpareto,
> and I have 20 pdf files for pareto/genpareto/genextreme open)
>
> Josef
>
>
Josef,

The reference for that particular estimator is
http://research.microsoft.com/en-us/um/people/minka/papers/minka-gamma.pdf

There is another estimator that I have used that came from a very good
'statistics for meteorologists' book, but I don't have that on me.  I can
get it to you tomorrow, though.

Ben Root
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