Integral curve fitting in origin

[`Pavol Namer]

Dear users,

I deal with following problem.

I've got a data of Intenzity of chemiluminezcence as a function of temperature. The data should be fitted by following equation:

I found that in origin one can fit also data with integral function, with fittin parameters P, A, i, E.
The beta and R are constants that I already know.

So my question is. Is it possible to make this kind of curve fitting in Origin, and Is it correct to make this kind of curve fitting or it is impossible to obtain correct physical results.

Thank you in advance

PN

 

[JJacquelin]

Hi ! Your question concerns the fitting of an "integral equation" to experimental data.
I cannot say, a-priori, if it's relevant to the kind of method used in the paper : https://fr.scribd.com/doc/14674814/Regressions-et-equations-intégrales
To answer to this question, it is important to know how the experimental data are distributed (regularly or non-regularly spaced, range, order of magnitude of scatter, ...).
If you post an example of data, I could check and say if the method described in the referenced paper can be addapted to become convenient in your case.

 

[`Pavol Namer]

Hi!
Thank you for your answer,
Of course, I can show you the data,

so, here's the plot of a data and data below

303,143 0,40355
303,143 0,88781
303,143 0,32284
303,143 0,64568
303,143 0,88781
303,143 0,32284
303,143 0,88781
303,143 0,16142
303,143 0,48426
303,143 0,64568
303,143 0,72639
303,143 0,64568
303,143 0,40355
303,143 0,48426
303,143 1,21065
303,143 0,72639
303,143 2,25989
303,143 0,24213
303,143 0,48426
303,143 0,64568
303,143 0,48426
303,143 0,72639
303,143 0,56497
303,143 0,72639
303,143 0,56497
303,143 0,32284
303,143 0,40355
303,143 0,40355
303,143 0,56497
303,143 0,40355
303,143 0,40355
303,143 0,88781
303,143 0,72639
303,143 0,88781
303,143 0,24213
303,143 0,64568
303,143 0,48426
303,143 0,8071
303,143 0,40355
303,143 0,40355
303,143 0,16142
303,143 0,16142
303,143 0,56497
303,143 0,56497
303,143 0,48426
303,143 1,12994
303,143 0,40355
303,143 0,8071
303,143 0,56497
303,143 0,96852
303,143 0,32284
303,143 0,81517
303,143 0,64568
303,143 0,72639
303,143 0,48426
303,143 0,56497
303,143 0,8071
303,143 0,32284
303,143 0,24213
303,143 0,72639
303,297 0,72639
303,469 0,64568
303,64 0,32284
303,812 0,96852
303,983 0,56497
304,155 1,04923
304,326 0,08071
304,498 0,24213
304,67 0,72639
304,841 0,56497
305,013 0,40355
305,184 0,8071
305,356 0,8071
305,527 0,72639
305,699 0,32284
305,87 0,64568
306,042 0,88781
306,213 0,56497
306,384 0,56497
306,556 0,48426
306,727 0,8071
306,899 0,56497
307,07 0,48426
307,241 0,8071
307,413 0,88781
307,584 0,48426
307,756 0,56497
307,927 0,40355
308,098 0,32284
308,27 0,24213
308,441 0,48426
308,612 0,48426
308,784 0,72639
308,955 0,24213
309,126 0,56497
309,297 0,32284
309,469 0,32284
309,64 0,48426
309,811 0,88781
309,982 0,72639
310,154 0,96852
310,325 0,56497
310,496 0,24213
310,667 0,48426
310,839 0,72639
311,01 0,88781
311,181 0,24213
311,352 0,56497
311,523 0,8071
311,694 0,88781
311,865 0,24213
312,037 0,8071
312,208 0,72639
312,379 0,40355
312,55 0,56497
312,721 0,88781
312,892 0,56497
313,063 0,24213
313,234 0,64568
313,405 0,32284
313,576 0,40355
313,747 1,21065
313,918 0,96852
314,089 0,56497
314,26 0,88781
314,431 0,40355
314,602 0,08071
314,773 0,64568
314,944 0,40355
315,115 0,08071
315,286 0,64568
315,457 0,64568
315,628 1,21065
315,799 0,48426
315,97 0,32284
316,141 0,56497
316,312 0,8071
316,482 0,8071
316,653 0,56497
316,824 0,24213
316,995 0,32284
317,166 0,88781
317,337 0,40355
317,508 0,40355
317,678 0,24213
317,849 0,32284
318,02 1,04923
318,191 0,32284
318,361 0,24213
318,532 0,40355
318,703 0,56497
318,874 0,56497
319,044 0,32284
319,215 0,40355
319,386 0,72639
319,557 0,72639
319,727 0,56497
319,898 0,8071
320,069 0,64568
320,239 0,56497
320,41 0,40355
320,581 0,32284
320,751 0,56497
320,922 0,64568
321,092 0,32284
321,263 0,56497
321,434 0,96852
321,604 0,48426
321,775 0,32284
321,945 0,56497
322,116 0,8071
322,287 0,64568
322,457 0,64568
322,628 0,64568
322,798 0,56497
322,969 0,64568
323,139 0,48426
323,31 0,40355
323,48 0,64568
323,651 0,64568
323,821 0,64568
323,991 0,32284
324,162 0,48426
324,332 0,48426
324,503 0,16142
324,673 0,96852
324,844 0,8071
325,014 0,24213
325,184 0,72639
325,355 0,32284
325,525 0,48426
325,695 0,8071
325,866 0,88781
326,036 0,64568
326,207 0,96852
326,377 0,4891
326,547 0,96852
326,717 0,48426
326,888 0,64568
327,058 0,40355
327,228 0,40355
327,399 0,16142
327,569 0,40355
327,739 0,40355
327,909 0,40355
328,079 0,8071
328,25 0,32284
328,42 0,40355
328,59 0,48426
328,76 0,56497
328,93 0,8071
329,101 1,85634
329,271 0,40355
329,441 0,56497
329,611 0,48426
329,781 0,48426
329,951 0,64568
330,121 0,56497
330,291 0,72639
330,462 0,64568
330,632 0,40355
330,802 0,64568
330,972 0,48426
331,142 1,04923
331,312 0,88781
331,482 1,12994
331,652 1,04923
331,822 0,48426
331,992 0,56497
332,162 0,8071
332,332 0,56497
332,502 0,8071
332,672 0,64568
332,842 0,32284
333,012 0,88781
333,182 0,8071
333,352 0,8071
333,522 0,32284
333,691 0,88781
333,861 0,72639
334,031 0,88781
334,201 0,72639
334,371 0,32284
334,541 0,32284
334,711 0,88781
334,881 0,72639
335,05 0,64568
335,22 0,40355
335,39 0,64568
335,56 0,24213
335,73 0,56497
335,899 0,88781
336,069 0,40355
336,239 0,32284
336,409 0,8071
336,578 0,96852
336,748 0,96852
336,918 0,8071
337,088 0,72639
337,257 0,48426
337,427 0,72639
337,597 0,48426
337,766 0,40355
337,936 0,56497
338,106 0,40355
338,275 1,21065
338,445 0,48426
338,615 0,88781
338,784 0,88781
338,954 0,56497
339,123 0,64568
339,293 0,40355
339,463 0,72639
339,632 1,21065
339,802 0,56497
339,971 1,21065
340,141 0,48426
340,31 0,56497
340,48 0,72639
340,649 0,72639
340,819 0,64568
340,988 0,64568
341,158 0,88781
341,327 1,04923
341,497 1,12994
341,683 1,04923
341,836 0,56497
342,005 0,88781
342,191 0,40355
342,361 0,64568
342,53 0,48426
342,7 0,96852
342,869 0,72639
343,038 0,64568
343,191 0,64568
343,36 0,56497
343,53 0,48426
343,699 0,88781
343,868 0,56497
344,054 1,04923
344,207 0,88781
344,376 0,96852
344,545 0,72639
344,715 0,88781
344,901 0,8071
345,053 2,17918
345,223 0,96852
345,392 1,21065
345,578 0,8071
345,73 0,72639
345,899 1,53349
346,086 0,64568
346,255 1,53349
346,424 0,88781
346,593 0,96852
346,762 0,96852
346,931 0,72639
347,101 0,8071
347,27 0,72639
347,439 0,96852
347,608 1,21065
347,777 1,12994
347,946 0,96852
348,115 0,96852
348,284 0,96852
348,453 1,12994
348,622 0,56497
348,792 1,04923
348,961 1,12994
349,13 0,8071
349,299 0,72639
349,468 1,37207
349,637 0,88781
349,806 0,81517
349,975 1,03874
350,144 0,32607
350,313 0,8071
350,482 0,8071
350,65 1,12994
350,819 0,8071
350,988 0,88781
351,157 0,72639
351,326 1,04923
351,495 1,21065
351,664 1,04923
351,833 1,29136
352,002 0,72639
352,171 1,21065
352,339 0,96852
352,508 0,72639
352,677 1,21065
352,846 0,56497
353,015 1,21065
353,183 0,40355
353,352 1,69492
353,521 0,8071
353,69 0,64568
353,859 0,40355
354,027 1,29136
354,196 1,21065
354,365 1,12994
354,534 0,88781
354,702 1,37207
354,871 0,72639
355,04 0,64568
355,208 0,88781
355,377 1,12994
355,546 0,8071
355,714 1,21065
355,883 0,88781
356,052 1,04923
356,22 1,04923
356,389 1,12994
356,558 1,12994
356,726 1,12994
356,895 1,69492
357,063 0,96852
357,232 1,29136
357,4 1,29136
357,569 0,96852
357,738 0,96852
357,906 1,45278
358,075 1,04923
358,243 1,12994
358,412 0,8071
358,58 0,40355
358,749 0,96852
358,917 1,04923
359,085 1,04923
359,254 1,37207
359,422 0,56497
359,591 1,21065
359,759 0,64568
359,928 1,61421
360,096 1,12994
360,264 1,85634
360,433 1,12994
360,601 0,72639
360,77 0,8071
360,938 1,04923
361,106 1,37207
361,275 2,01776
361,443 1,12994
361,611 1,04923
361,78 1,12994
361,948 0,88781
362,116 1,21065
362,285 1,53349
362,453 1,45278
362,621 1,77563
362,789 1,53349
362,958 1,29136
363,126 0,72639
363,294 1,77563
363,462 1,29136
363,63 0,8071
363,799 1,77563
363,967 1,93705
364,135 1,77563
364,303 1,45278
364,471 1,77563
364,639 1,45278
364,808 1,21065
364,976 1,21065
365,144 1,29136
365,312 1,37207
365,48 1,53349
365,648 1,12994
365,816 1,12994
365,984 1,12994
366,152 1,45278
366,32 1,93705
366,488 1,69492
366,657 1,12994
366,825 1,53349
366,993 1,29136
367,161 1,45278
367,329 1,21065
367,497 1,85634
367,665 1,21065
367,832 1,77563
368 1,53349
368,168 1,93705
368,336 2,42131
368,504 1,93705
368,672 1,21065
368,84 2,01776
369,008 1,93705
369,176 2,01776
369,344 2,01776
369,512 1,45278
369,679 1,77563
369,847 2,09847
370,015 1,12994
370,183 1,85634
370,351 2,50202
370,519 2,25989
370,686 2,01776
370,854 2,42131
371,022 2,01776
371,19 2,25989
371,358 1,53349
371,525 2,09847
371,693 2,01776
371,861 2,17918
372,029 1,77563
372,196 2,01776
372,364 1,45278
372,532 2,09847
372,699 2,50202
372,867 2,17918
373,035 3,22841
373,202 1,53349
373,37 1,85634
373,538 2,98628
373,705 1,71186
373,873 2,74415
374,04 1,85634
374,208 1,37207
374,376 1,29136
374,543 2,50202
374,711 1,77563
374,878 2,42131
375,046 1,85634
375,213 2,42131
375,381 1,61421
375,549 2,58273
375,716 2,42131
375,884 2,25989
376,051 2,82486
376,219 2,17918
376,386 2,3406
376,554 2,50202
376,721 2,82486
376,888 1,69492
377,056 1,93705
377,223 1,69492
377,391 2,01776
377,558 1,69492
377,726 2,66344
377,893 2,90557
378,06 3,47054
378,228 2,25989
378,395 3,30912
378,562 2,98628
378,73 2,3406
378,897 2,25989
379,064 2,17918
379,232 2,3406
379,399 2,90557
379,566 2,98628
379,734 2,58273
379,901 2,42131
380,068 2,90557
380,235 2,17918
380,403 2,74415
380,57 2,3406
380,737 3,38983
380,904 3,06699
381,072 2,98628
381,239 2,50202
381,406 2,50202
381,573 3,06699
381,74 2,58273
381,907 3,63196
382,075 3,55125
382,242 4,19693
382,409 2,82486
382,576 2,98628
382,743 3,30912
382,91 3,63196
383,077 3,22841
383,244 3,22841
383,411 2,66344
383,578 2,98628
383,746 4,35835
383,913 2,98628
384,08 3,30912
384,247 3,38983
384,414 3,47054
384,581 3,55125
384,748 4,43906
384,915 4,11622
385,082 4,27764
385,249 3,87409
385,416 2,82486
385,583 3,71267
385,749 3,71267
385,916 3,22841
386,083 3,22841
386,25 5,08475
386,417 3,87409
386,584 4,27764
386,751 4,03551
386,918 3,71267
387,085 3,71267
387,251 4,27764
387,418 3,63196
387,585 4,03551
387,752 5,08475
387,919 4,7619
388,086 4,60048
388,252 4,27764
388,419 3,30912
388,586 3,79338
388,753 3,71267
388,919 3,87409
389,086 4,35835
389,253 5,32688
389,42 4,68119
389,586 4,19693
389,753 5,32688
389,92 4,03551
390,087 4,27764
390,253 6,21469
390,42 4,35835
390,587 4,68119
390,753 5,08475
390,92 4,60048
391,086 4,68119
391,253 4,43906
391,42 6,21469
391,586 5,08475
391,753 4,43906
391,919 5,4883
392,086 5,00404
392,253 5,73043
392,419 5,4883
392,586 7,42534
392,752 5,00404
392,919 6,21469
393,085 7,02179
393,252 5,32688
393,418 6,05327
393,585 5,4883
393,751 7,26392
393,918 4,92333
394,084 5,64972
394,251 6,61824
394,417 5,40759
394,584 5,89185
394,75 6,05327
394,916 5,24617
395,083 6,13398
395,249 5,81114
395,416 5,97256
395,582 6,13398
395,748 4,68119
395,915 7,34463
396,081 6,53753
396,247 6,69895
396,414 7,34463
396,58 5,97256
396,746 5,56901
396,913 7,74818
397,079 7,5004
397,245 8,15174
397,411 8,07103
397,578 8,31316
397,744 7,02179
397,91 6,2954
398,076 7,02179
398,243 8,31316
398,409 7,42534
398,575 7,50605
398,741 7,82889
398,907 7,58676
399,074 7,74818
399,24 6,69895
399,406 7,66747
399,572 7,26392
399,738 9,76594
399,904 8,23245
400,07 7,42534
400,236 6,94108
400,403 8,15174
400,569 8,47458
400,735 7,1025
400,901 8,23245
401,067 8,23245
401,233 7,99031
401,399 9,4431
401,565 9,68523
401,731 8,95884
401,897 8,15174
402,063 9,52381
402,229 8,55529
402,395 8,79742
402,561 8,55529
402,727 9,28168
402,893 8,636
403,059 8,79742
403,225 7,99031
403,391 9,28168
403,557 8,55529
403,722 9,20097
403,888 9,28168
404,054 10,08878
404,22 9,36239
404,386 10,2502
404,552 11,21872
404,718 9,84665
404,884 10,81517
405,049 10,73446
405,215 8,79742
405,381 11,46086
405,547 10,57304
405,713 9,60452
405,878 9,36239
406,044 10,89588
406,21 11,29944
406,376 11,38015
406,541 12,26796
406,707 12,02583
406,873 10,49233
407,038 12,42938
407,204 12,83293
407,37 11,70299
407,536 12,83293
407,701 11,21872
407,867 13,80145
408,033 12,18725
408,198 12,42938
408,364 11,21872
408,529 11,0573
408,695 12,02583
408,861 11,86441
409,026 13,64003
409,192 12,42938
409,357 13,3979
409,523 10,00807
409,689 13,31719
409,854 11,29944
410,02 14,28571
410,185 11,86441
410,351 14,28571
410,516 13,64003
410,682 13,47861
410,847 11,54157
411,013 13,55932
411,178 12,18725
411,344 13,72074
411,509 11,21872
411,675 14,60856
411,84 13,64003
412,005 12,99435
412,171 15,25424
412,336 13,55932
412,502 14,28571
412,667 14,28571
412,832 14,04358
412,998 14,04358
413,163 16,5456
413,328 14,36642
413,494 13,64003
413,659 15,17353
413,824 14,52785
413,99 15,17353
414,155 14,04358
414,32 15,81921
414,486 16,46489
414,651 18,15981
414,816 15,65779
414,981 15,01211
415,147 17,75626
415,312 16,06134
415,477 16,38418
415,642 15,98063
415,807 15,89992
415,973 15,01211
416,138 17,02986
416,303 17,3527
416,468 15,98063
416,633 15,89992
416,798 16,62631
416,964 17,67554
417,129 20,01614
417,294 17,51412
417,459 20,17756
417,624 18,40194
417,789 17,75626
417,954 19,93543
418,119 18,64407
418,284 20,82324
418,449 20,41969
418,614 17,11057
418,779 18,80549
418,944 18,64407
419,109 21,63035
419,274 19,77401
419,439 21,71106
419,604 20,58111
419,769 21,30751
419,934 19,37046
420,099 22,0339
420,264 20,58111
420,429 20,82324
420,594 22,51816
420,759 24,61663
420,924 23,08313
421,089 24,29379
421,254 21,30751
421,419 25,50444
421,584 22,51816
421,748 23,80952
421,913 22,27603
422,078 22,59887
422,243 23,56739
422,408 25,35432
422,573 24,3745
422,737 24,29379
422,902 25,58515
423,067 27,19935
423,232 28,16788
423,396 24,45521
423,561 27,28006
423,726 27,84504
423,891 28,65214
424,055 30,18563
424,22 30,6699
424,385 30,34705
424,549 32,92978
424,714 29,9435
424,879 31,39629
425,043 31,63842
425,208 29,86279
425,373 31,63842
425,537 31,71913
425,702 31,31558
425,867 32,2841
426,031 35,02825
426,196 31,96126
426,36 34,6247
426,525 37,61098
426,69 32,60694
426,854 33,65617
427,019 31,15416
427,183 34,94754
427,348 35,99677
427,512 38,66021
427,677 36,31961
427,841 37,046
428,006 39,3866
428,17 39,30589
428,335 41,56578
428,499 40,67797
428,664 40,03228
428,828 41,40436
428,993 43,17998
429,157 46,16626
429,321 40,1937
429,486 43,98709
429,65 40,67797
429,815 43,50282
429,979 41,96933
430,143 43,98709
430,308 45,60129
430,472 44,0678
430,636 46,73123
430,801 51,49314
430,965 47,2155
431,129 49,47538
431,294 46,89266
431,458 51,57385
431,622 49,31396
431,787 50,60533
431,951 54,88297
432,115 52,38095
432,279 52,46166
432,444 56,33575
432,608 57,54641
432,772 60,37127
432,936 54,72155
433,1 57,38499
433,265 59,24132
433,429 57,30428
433,593 60,29056
433,757 62,06618
433,921 63,68039
434,085 65,29459
434,249 68,11945
434,414 64,97175
434,578 64,24536
434,742 68,84584
434,906 67,63519
435,07 69,3301
435,234 71,18644
435,398 70,37934
435,562 72,80065
435,726 76,67474
435,89 81,03309
436,054 73,93059
436,218 73,12349
436,382 79,09605
436,546 74,73769
436,71 81,9209
436,874 86,27926
437,038 84,82647
437,202 82,56659
437,366 89,50767
437,53 94,10815
437,694 91,12187
437,858 94,83454
438,022 93,94673
438,186 98,30508
438,35 99,03148
438,513 96,0452
438,677 95,39952
438,841 104,7619
439,005 105,08475
439,169 104,7619
439,333 107,82889
439,496 110,73446
439,66 108,23245
439,824 115,65779
439,988 115,65779
440,152 118,8862
440,315 120,90395
440,479 119,28975
440,643 118,72478
440,807 123,24455
440,97 124,53592
441,134 130,34705
441,298 130,10492
441,462 135,67393
441,625 133,17191
441,789 132,12268
441,953 140,75868
442,116 144,14851
442,28 149,55609
442,444 143,90638
442,607 150,68604
442,771 149,39467
442,934 158,59564
443,098 158,99919
443,262 156,49718
443,425 163,59968
443,589 164,24536
443,752 165,94027
443,916 170,13721
444,08 167,07022
444,243 179,4996
444,407 179,90315
444,57 178,45036
444,734 192,81679
444,897 190,5569
445,061 195,64165
445,224 198,14366
445,388 193,86602
445,551 199,83858
445,715 198,78935
445,878 196,93301
446,041 207,50605
446,205 221,2268
446,368 205,73043
446,532 213,96287
446,695 218,96691
446,858 215,98063
447,022 217,99839
447,185 218,15981
447,349 234,8749
447,512 230,26634
447,675 241,64649
447,839 232,92978
448,002 244,8749
448,165 248,91041
448,329 252,7845
448,492 250,84746
448,655 257,70783
448,818 253,5109
448,982 253,10734
449,145 265,94027
449,308 263,92252
449,471 257,54641
449,635 283,53511
449,798 276,99758
449,961 291,52542
450,124 294,26957
450,287 287,4092
450,451 283,4544
450,614 286,19855
450,777 308,55529
450,94 298,14366
451,103 309,36239
451,266 310,49233
451,429 306,77966
451,593 318,0791
451,756 324,69734
451,919 322,841
452,082 322,841
452,245 337,69169
452,408 340,43584
452,571 342,5343
452,734 342,45359
452,897 354,88297
453,06 361,50121
453,223 360,77482
453,386 376,59403
453,549 377,9661
453,712 385,55287
453,875 386,11784
454,038 388,70056
454,201 414,68927
454,364 412,42938
454,527 412,75222
454,69 429,53995
454,853 439,79015
455,016 432,84907
455,179 452,62308
455,341 462,06618
455,504 462,954
455,667 480,79096
455,83 483,93866
455,993 495,2381
456,156 495,56094
456,319 504,19693
456,481 520,33898
456,644 536,31961
456,807 557,14286
456,97 556,33575
457,133 570,94431
457,295 576,3519
457,458 591,84826
457,621 595,88378
457,784 622,92171
457,946 622,27603
458,109 657,86925
458,272 664,32607
458,435 673,68846
458,597 687,48991
458,76 698,14366
458,923 720,5004
459,085 745,76271
459,248 762,63115
459,411 773,76917
459,573 785,23002
459,736 798,38579
459,898 810,16949
460,061 851,41243
460,24 861,82405
460,386 883,05085
460,549 896,20662
460,711 928,00646
460,874 942,85714
461,037 965,94027
461,215 991,92897
461,378 1026,55367
461,54 1031,63842
461,703 1068,44229
461,865 1073,12349
462,028 1099,1929
462,19 1117,91768
462,353 1132,76836
462,515 1142,13075
462,678 1203,38983
462,84 1220,5004
463,003 1234,54399
463,165 1256,98144
463,328 1267,47377
463,49 1285,95642
463,652 1323,80952
463,815 1345,84342
463,977 1335,51251
464,14 1351,08959
464,302 1384,74576
464,464 1387,97417
464,627 1431,71913
464,789 1431,88055
464,951 1464,5682
465,114 1464,5682
465,276 1472,55851
465,438 1490,07264
465,6 1511,21872
465,763 1528,00646
465,925 1540,51655
466,087 1582,80872
466,249 1564,81033
466,412 1595,15738
466,574 1613,15577
466,736 1623,56739
466,898 1636,40032
467,061 1671,50928
467,223 1674,41485
467,385 1682,48588
467,547 1706,86037
467,709 1757,4657
467,871 1768,20016
468,034 1780,06457
468,196 1766,66667
468,358 1815,98063
468,52 1812,75222
468,682 1829,78208
468,844 1864,89104
469,006 1859,48345
469,168 1883,53511
469,33 1887,00565
469,492 1899,03148
469,654 1955,52865
469,816 1970,54076
469,978 1954,56013
470,14 2005,40759
470,302 2013,47861
470,464 2045,52058
470,626 2077,159
470,788 2060,45198
470,95 2111,0573
471,112 2093,13963
471,274 2186,68281
471,436 2180,87167
471,598 2195,40032
471,76 2231,71913
471,922 2239,14447
472,084 2267,07022
472,246 2287,73204
472,408 2294,26957
472,57 2337,69169
472,731 2358,91848
472,893 2413,64003
473,055 2433,0912
473,063 2452,46166

I don't know if you mean this kind of data example, do you?

 

[JJacquelin]

At first sight, it doesn't work.
What is the value of T_room corresponding to the data ?
Is the unknown coefficient (A/i) negative ?

 

[`Pavol Namer]

Hi,
The Troom is the initial temperature so it start in first column Troo=303,143 Kelvin
A/i is pozitive parameter and parameter Beta is also pozitive (beta value is known, so it is not fit).

Thank you for your help.

P.

Here is a similar plot where the data was fitted on this type of file using equastion writes above

 

[JJacquelin]

When T is increassing, the integral is increassing, the denominator of the function is increassing, the function is decreassing, which is not consistent with the data. This seems to be the main cause of failure of the fitting.

 

[JJacquelin]

Since the issue remained outstanding for enough time, I will close it, as far I am concerned.
I cannot help more because the function proposed is not convenient to fit with the given data : any fitting method fails if the general shape of the function is in contradiction with the experimental data.
This is clear on the joint figure : The 1080 experimental points are drawn on logarithmic scale. This is necessary to make visible the scatter in case of large range of magnitude.
The kind of shape of the functions I(T) is sketched (red curve) It is not possible to compute the values of the parameters because there is no experimental point in the convenient range. So, the curve drawn is purely symbolic, only for explanation.
Probably, reconsidering the physical model will lead to a more convenient function.

 

[`Pavol Namer]

I´m so sorry, that I haven't replied earlier. Thank you for sharing your answer, but If you look at my first contribution you have used different formula from my formula in your plot. The denominator is power of 2. But you are right this function has decrease character. And therefore we have to used different physical model.

Thank's a lot for your time, and again I am very sorry that I haven't replied earlier.

 

[JJacquelin]

Hi Pavol Namer !
I used the formula with denominator at power 2. In fact, there is a typo on the figure attached to my answer : I forgot to write the power. It doesn't matter since it was only a skeched graph.