| Author |
 Topic  |
|
|
dafekare
USA
12 Posts |
 Posted - 04/28/2023 : 3:20:51 PM
|
Hello Team,
This is a follow-up message to one of my previous requests. In the figure attached, the red curve appears as a normal distribution so it's reasonable to apply a Gaussian fit, but what about the green and blue curves which appear left skewed? Is it still OK to use the Gaussian fit values for them and rely on the reported values? Or is there a way to apply non-linear fitting to a trimodal distribution like this that has seem to have a mix of Gaussian-type and left-skewed-type functional behaviors?
Please advise.
DAA |
|
|
YimingChen
1664 Posts |
Posted - 04/28/2023 : 5:22:44 PM
|
The x-axis is not linear on your graph. So you see the peak left skewed.
James
|
 |
|
|
aplotnikov
Germany
169 Posts |
Posted - 04/29/2023 : 04:35:20 AM
|
| The demonstrated curve evidently represents an overlap of two log-normal peaks. |
|
|
|
dafekare
USA
12 Posts |
Posted - 05/01/2023 : 09:28:55 AM
|
Thank you both for the replies. I know the left axis is log spaced. Are you both saying it's OK to use the results then?
DAA |
|
|
|
aplotnikov
Germany
169 Posts |
Posted - 05/02/2023 : 06:32:35 AM
|
| The X-axis is logarithmic, not the left Y one! You have normally distributed logarithm of particle size that is typical for grain refinement processes - as distinct to the case of particle growth with nucleation. |
|
|
|
dafekare
USA
12 Posts |
Posted - 05/03/2023 : 1:54:27 PM
|
I'm sorry for the confusion. I meant the X axis is log spaced. Thank you for the background information. But I need more clarity please. It appears a population of particles with a log normal distribution in general may contain subset of particle populations that deviate from log normality and can be L- or R-skewed - as in this case. Given that this can be true (please correct otherwise), is it then statistically reasonable to depend on the output parameters like Xc and W from this my fitting approach for both the skewed and log-normal particle populations? That's my main question here.
Many thanks in advance!
DAA |
|
|
|
YimingChen
1664 Posts |
Posted - 05/03/2023 : 2:26:21 PM
|
I am not convinced that using a log-normal function is necessary for the fitting of the data. The three fitted peaks appear to be left-skewed because it is plotted with a log scale on the x-axis. I would suggest changing the x-axis to a linear scale and fitting the data with a Gaussian. This should produce the same results while also ensuring that the fitted peaks are symmetric.
|
Edited by - YimingChen on 05/03/2023 2:26:51 PM |
|
|
|
aplotnikov
Germany
169 Posts |
Posted - 05/03/2023 : 5:09:40 PM
|
If you see normally distributed data in the graph with logarithmic x-axis that means undoubtedly, your particle sizes are distributed according the log-normal law. With no any other variants. It is absolutely clear and should be not discussed further. But surely you can try numerous fit functions with absolutely predictable results. Why just not to try to approximate yor data by a superposition of two log-normal peaks???
2YimingChen: The measured peaks ARE NOT symmetric if x-axis is linear. There is no any reason to use symmetric distributions for the approximation. |
|
|
|
YimingChen
1664 Posts |
Posted - 05/04/2023 : 09:13:31 AM
|
| The conclusion that the measurements are symmetric under a linear x scale is all based on the fitting result. The three Gaussian peak functions could fit the data with high R-squared values. But if it is confirmed the physics process of generating the distribution curve follows a log-normal, then it is recommended to use log-normal peak fitting. |
|
|
|
aplotnikov
Germany
169 Posts |
Posted - 05/04/2023 : 10:24:32 AM
|
quote:
Originally posted by YimingChen
The conclusion that the measurements are symmetric under a linear x scale is all based on the fitting result.
Nope. It is based on the form of the measured peaks only. It is quite evident. Just try to replot the demonstrated curves using linear x-axis. Or just try to plot ANY log-normal peak using logarithmic x-axis. :)
It may be surprising for the topic starter that normal distribution is quite uncommon in the real life. But it is true. And sometimes it requires certain efforts to transform your data if you are going to use common statistical approaches suitable for normally distributed data (e.g., by projecting fitted Jonson's S-distributions, by bootstrapping, etc.). But log-normal distribution is rather typical in the world of particle sizing reflecting certain mechanisms of particle formation. |
Edited by - aplotnikov on 05/04/2023 10:26:49 AM |
|
|
| |
Topic |
|
Interpreting multimodal distributions