[SciPy-User] [Numpy-discussion] Fitting a curve on a log-normal distributed data
Tue Nov 17 13:36:36 CST 2009
On Tue, Nov 17, 2009 at 12:57 PM, Robert Kern <firstname.lastname@example.org> wrote:
> On Tue, Nov 17, 2009 at 12:38, <email@example.com> wrote:
> > So, it's not clear to me what you really want, or what your sample data
> > looks like (do you have only one 15 element sample or lots of them).
> I'm guessing that they aren't really samples of (conc, size) pairs so
> much as binned data.
Correct. These are discrete sample points.
> Particles with sizes between 0.1 and 0.3 um (for
> example; I don't know where the bin edges actually are in his data)
> have a concentration of 119.7681 particles/<some unit of volume>.
True, in particles/cm^3 units
> This can be normalized to a more proper histogrammed distribution, except
> that the lower end of the distribution below 0.1 um has been censored
> by his measuring process. He then wants to infer the continuous
> distribution that generated that censored histogram so he can predict
> what the distribution is in the censored region.
Exactly. Where later I am hoping to find a critical size point using another
integrating upwards to obtain total concentration from that point on and do
with another instrument.
The 0.1 um threshold comes from the instrument limit. It can't measure below
due to the constraint of the Mie scattering theory.
> So, I would say that it's a bit trickier than fitting the log-normal
> PDF to the data for a couple of reasons.
> 1) Directly fitting PDFs to histogram values is usually not a great
> idea to begin with.
> 2) We don't know how much probability mass is in the censored region.
So we agree that it is easy to implement a log-normal fit than a discrete
> Robert Kern
> "I have come to believe that the whole world is an enigma, a harmless
> enigma that is made terrible by our own mad attempt to interpret it as
> though it had an underlying truth."
> -- Umberto Eco
> SciPy-User mailing list
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