# Help with probability distribution for description of particle sizes

1. Aug 10, 2011

### katkak

I study nanoparticles. Basically, they are prepared by being "etched away" from larger chunks of material. I need to describe their sizes, i.e. fit the histogram of measured sizes, with a probability distribution. The measured distribution is clearly asymmetrical with a tail toward larger sizes (see the attached picture, histograms with much higher numbers of occurrences have basically the same shape).

(i) Which probability distribution is suitable for the description of these data?

When trying to fit the data using common distributions (Gauss/Lorentz clearly don't fit very well, lognormal), Poisson seems to be the best match (just judging from the shape).

(ii) Should the distribution be discrete or continuous?

At such small sizes (4 nm) the crystal lattice constant (0.54 nm) becomes significant (i.e. approx. 8 crystal lattices per particle), but the size is also influenced by the rearrangement of atoms at the surface and the surface termination. So, the size is not just "integer multiple" of the crystal lattice constant.

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• ###### Graph1-ostre.jpg
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2. Aug 10, 2011

### bpet

(this questions belongs in the stats forum)

Have you tried the Gamma distribution?

3. Aug 11, 2011

### katkak

Thanks, seems to be quite nice. I didn't know this distribution. Is it "natural" for a size distribution to behave as Gamma distribution?

4. Aug 11, 2011

### bpet

Well, for integer shape parameters the gamma distribution can be interpreted as a sum of exponential random variables so I don't know if that helps.

Also, are you sure the distribution is not lognormal?

5. Aug 11, 2011

### katkak

I tried the lognormal fit again using a different command in the software (I use Origin, which is sometimes a bit unpredictable) and it doesn't not seem so bad. I'll try to do some more fitting with different datasets and see which distribution fits better.

Thanks a lot.