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

Gökhan Sever gokhansever@gmail....
Sat Nov 21 15:57:10 CST 2009

One more update on this subject. I have been looking through some of the
papers on this topic, and I have finally found exactly what I need in this

Hussein, T., Dal Maso, M., Petaja, T., Koponen, I. K., Paatero, P., Aalto,
P. P., Hameri, K., and Kulmala, M.: Evaluation of an automatic algorithm for
fitting the particle number size distributions, Boreal Environ. Res., 10,
337–355, 2005.

Here is the abstract:

"The multi log-normal distribution function is widely in use to parameterize
the aerosol particle size distributions. The main purpose of such a
parameterization is to quantitatively describe size distributions and to
allow straightforward comparisons between different aerosol particle data
sets. In this study, we developed and evaluated an algorithm to parameterize
aerosol particle number size distributions with the multi log-normal
distribution function. The current algorithm is automatic and does not need
a user decision for the initial input parameters; it requires only the
maximum number of possible modes and then it reduces this number, if
possible, without affecting the fitting quality. The reduction of the number
of modes is based on an overlapping test between adjacent modes. The
algorithm was evaluated against a previous algorithm that can be considered
as a standard procedure. It was also evaluated against a long-term data set
and different types of measured aerosol particle size distributions in the
ambient atmosphere. The evaluation of the current algorithm showed the
following advantages: (I) it is suitable for different types of aerosol
particles observed in different environments and conditions, (2) it showed
agreement with the previous standard algorithm in about 90% of long-term
data set, (3) it is not time-consuming, particularly when long-term data
sets are analyzed, and (4) it is a useful tool in the studies of atmospheric
aerosol particle formation and transformation."

The full-text is freely available at:

On Mon, Nov 16, 2009 at 11:44 PM, Gökhan Sever <gokhansever@gmail.com>wrote:

> Hello,
> I have a data which represents aerosol size distribution in between 0.1 to
> 3.0 micrometer ranges. I would like extrapolate the lower size down to 10
> nm. The data in this context is log-normally distributed. Therefore I am
> looking a way to fit a log-normal curve onto my data. Could you please give
> me some pointers to solve this problem?
> Thank you.
> --
> Gökhan

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