| Author |
 Topic  |
|
|
philip.94@live.it
Italy
1 Posts |
 Posted - 06/28/2018 : 10:34:56 AM
|
Origin Ver. and Service Release: OriginPro /Evaluation 2018b 64Bit
Operating System: Windows 10
Hy guys,
I'm trying to do the fitting of a set of histograms with the LogNormal distribution in OriginPro.
I found that there are two methods for doing that, so I wanted to compare them, but still there is something I don't understand.
First method: manual creation of the histogram with the desired binning and then curve fitting with Analysis->Fitting->Nonlinear curve fit; here I select LogNormal and fix the param y0=0; I know that this method is based on Least Squares.
Second method: LogNormal fitting directly on raw data with Statistics->Descriptive Statistics->Distribution fit; I know that this method is based on Maximum Likelihood.
My data are values of oxygen tension (natural numbers).
I compared the two methods using two different bin widths: 1 and 2.5; this was easy to set with the first method, but with the second method I have done this: for bins of width 1 I just did directly the fitting of the data (this method is working on the raw data, but I'm supposing that it is anyway creating an histogram of the data and, since they are natural numbers, it just divides them by steps of 1), while for bins of width 2.5 I rebinned the data, i.e. I divided the data in bins of width 2.5 (outside Origin) and assigned for each of them the mid value of the bin they belong to; this last step was done just for a direct comparison with the LS method, I know it is a bit forced.
Results:
-for the second method (ML) changing the bins does not take to significative changes in the results, i.e. the fits are similar and the parameters of the LogNormal are very close to each other
-with the first method the fits are different and also with different heigths when compared with the ML method; I had to multiply them by a factor 4 and 2 respectively to compare them with the ML method.
Then I have some questions:
-How does the ML method treat the raw data to create the histograms on which to do the fits?
-Why the histograms/fits have different heigths if the binning should be the same?
-What is the best choice for fitting histograms and why?
I will appreciate any help! |
|
|
Shirley_GZ
China
Posts |
Posted - 06/29/2018 : 05:28:09 AM
|
Hi Philip,
For the questions you asked,
- The ML method doesn't need to bin the data. It estimates the value of the parameters, and then according to the bin user set, use the PDF(Probability density function, https://www.originlab.com/doc/Origin-Help/distribution-fit-Algorithm#PDF_2) to calculate the count of histogram.
- The ML method and Least Squares method have different algorithms, so the calculated parameters will be different.
- We think the ML method could be the better one, because it uses the raw data to do fit, in opposite, the Least Squares method fits from the binned data.
I hope these answers helps. If not, please let me know.
Thanks,
Shirley
Originlab Technical Service Team |
Edited by - Shirley_GZ on 06/29/2018 05:29:14 AM |
 |
|
| |
Topic |
|
|
|
Fit of histograms