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DataConv

Germany
60 Posts
Posted - 03/01/2022 :  04:03:46 AM  Show Profile  Edit Topic  Reply with Quote  View user's IP address  Delete Topic
Origin Ver. and Service Release (Select Help-->About Origin): OriginPro 2020
Operating System: W10P

In the fit functions menu, in the section 'Exponential', there is a formula named 'Stirling'. For my purposes it works nicely, but i need to know more about it. Has anyone a clue or even a reference, where this function is coming from (i guess from a person called 'Stirling')?
@OriginLab Corporation staff: I would be nice and good practice to mention the source of the functions/formula in a foot note of the related help. That helps e.g. in the scientific publication process...

Shirley_GZ

China
Posts
Posted - 03/01/2022 :  05:32:58 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi DataConv,

Yes, it is supposed to be a person name. Have you already read this help page to know the mathematical expression?
https://www.originlab.com/doc/Origin-Help/Stirling-FitFunc

Thanks,
Shirley



Originlab Technical Service Team
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DataConv

Germany
60 Posts
Posted - 03/01/2022 :  07:02:47 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Thank you Shirley.

Yes, and that is as much information i can get. There is a not so easy to find website where the same function is available, but the additional information provided there is also not helpful.
What i would need for further research is the full name - not just 'Stirling' - and best a publication/book aka reference, where the formula comes from. Using a fit function doesn't mean one understands it...
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ChaoC

USA
178 Posts
Posted - 03/01/2022 :  08:45:08 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi DataConv,

You can search for "James Stirling" or "Stirling's Approximation".
EDIT: See Sam's reply below

Chao
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DataConv

Germany
60 Posts
Posted - 03/01/2022 :  08:56:59 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hello ChaoC,

Please can you help me? Where is the connection between this specific fit function and the approximation for faculty of n (n!)? The two things seem to me like totally different cakes. And there are other Stirlings out there - like Stirling, W. Douglas?
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Sam Fang

293 Posts
Posted - 03/02/2022 :  02:58:55 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi DataConv,

Stirling function was proposed by Stirling, W.D in his paper: Algorithm AS212: Fitting the exponential curve by least squares. Appl. Stat., 34, 183-192.

It was better than the general form y=a+b*exp(c*x) because the latter tends to a+b when c->0 and it causes that a and b are not identifiable.

Sam
OriginLab Technical Services
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DataConv

Germany
60 Posts
Posted - 03/02/2022 :  06:30:41 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Thank you Sam,

... so i was on the right track. Just for those out there interested in the reference:
https://doi.org/10.2307/2347376
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