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

Robert Kern robert.kern@gmail....
Tue Nov 17 12:57:46 CST 2009

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. 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>. 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.

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.

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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