# [SciPy-User] [Numpy-discussion] Fitting a curve on a log-normal distributed data

Gökhan Sever gokhansever@gmail....
Tue Nov 17 13:36:36 CST 2009

```On Tue, Nov 17, 2009 at 12:57 PM, Robert Kern <robert.kern@gmail.com> wrote:

> On Tue, Nov 17, 2009 at 12:38,  <josef.pktd@gmail.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
equation, and
integrating upwards to obtain total concentration from that point on and do
a comparison
with another instrument.

The 0.1 um threshold comes from the instrument limit. It can't measure below
this level
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
one?

> --
> 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
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>

--
Gökhan
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