I'm working on the characterization of a nanoparticles system. I got size distributions like the one in the figure. It seems to me like a lognormal distribution, but could also be a sum of gaussian distributions. Can you give me a good reference about how to decide?
Thank you!
The log-normal distribution is important in the description of natural phenomena. The reason is that for many natural processes of growth, relative growth rate is independent of size. This is also known as Gibrat's law. It can be shown that a growth process following Gibrat's law will result in entity sizes with a log-normal distribution.
https://en.wikipedia.org/wiki/Particle-size_distribution
The profile you show looks like a Log-normal quite clearly. However, I think the final decision has to be taken after you fit with a log-normal and a Gaussian function, and compare the chi-square of each one.
If you don't have an a-priori model/reason to expect one or another, the best fitting procedure is the criterion for choosing.
Another reason is that you need MANY Gaussian functions and only ONE log-normal function to fit the data. Why choosing many fiting functions when you can have only one? Is there any reasonable basis for that?
Also, I tend to agree with Anurag Tyagi'c comment on the importance of what are you actually measuring. Finally, you won't fit this assymetric profile even with many Gaussian components, unles the 'many' turn into 'hundreds', but that makes no sense.
Hope this helps.
You may want to check the following discussion, where the physical basis for the particle size log-normal distribution is debated ─ «What is the origin of log-normal distribution in emulsion droplets and other particle systems?»: https://www.researchgate.net/post/What_is_the_origin_of_log-normal_distribution_in_emulsion_droplets_and_other_particle_systems
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