How to quantitatively compare particle distributions??

[#1]

Ok, so I have a large data set that has particle size distributions (surface area for each particle in the sample) for over 100 samples and I need a way to quantitatively (or semi-quantitatively) compare them to the whole data set or sort into groups with similar distribution characteristics.  The vast majority of the points are in the very small size fraction but due to the very small size do not contribute proportionally all that much to the total area.

I have attached sample plots of three representative samples with visually different distributions.

-Histograms of the raw data where the y axis is the particle size

-xy plots of the particle size (bin=x axis) vs the percentage that size bin contributes to the total area (y axis).  Two versions are shown, linear and log x axes (obviously log normal distributions here).

Eventually, these need to be visually comparable to one another (classes?) when the samples are plotted in real space relative to their collection point to delineate spatial patterns (purely visual).  I have been banging my head on this matter for weeks.  If anyone could help me I would be greatly obliged!

Thank you!

[#2]

How about comparing non-parametric distribution estimates of individual samples? Here is an example using the attached simulated data.

The report also comes with tests to see whether they are from the same distribution.

See Documentation: Life Distribution - Compare Groups 

[#3]

This is great, peng_liu.  I finally managed to replicate your script with my (monstrous) data set, but how do I get the group homogeneity tests?  Thanks!

[#4]

It is not far below the main plot. The outline node is closed by default. You need to open it to see the content.

[#5]

Hi @seismicfish ,

for starters i would stack the data, then you should have one column with the particle size and the other with the location (GS31, Gs32 and GS35). with that you can use some of the options in the Fit Y by X platform including densities and other visual options. Otherwise, the stacked data is also more useful in the graph builder.

send us a data sample if you want some inspiration.

ron

[#6]

Sounds good as I am not quite sure what you are explaining.  Here are some data to play with.  Thanks!

[#7]

Hi @seismicfish,

Please open the attached files and let us know if any of this is useful?

[#8]

These could be very helpful.  Thank you.  How did you translate all the data into a single column for both files though?

[#9]

I agree with @peng_liu about using Life Distribution to explore and test these distributions. I also recommend the Functional Data Explorer. This platform is for functional data, such as yours. You can learn more about it here.

[#10]

Dang.  The FDE looks like it may be the ticket but unfortunately I don't have JMP Pro, just standard.  Thanks though.