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 Build-In Fit Function 'Stirling'

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T O P I C    R E V I E W
DataConv Posted - 03/01/2022 : 04:03:46 AM
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...
6   L A T E S T    R E P L I E S    (Newest First)
DataConv Posted - 03/02/2022 : 06:30:41 AM
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
Sam Fang Posted - 03/02/2022 : 02:58:55 AM
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
DataConv Posted - 03/01/2022 : 08:56:59 AM
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?
ChaoC Posted - 03/01/2022 : 08:45:08 AM
Hi DataConv,

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

Chao
DataConv Posted - 03/01/2022 : 07:02:47 AM
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...
Shirley_GZ Posted - 03/01/2022 : 05:32:58 AM
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



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