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Fitting data avec une loi de puissance sigmoïde??

the physist
  • Mathématiques
    22 mai 2022 à 20:28:56

    Bonjour,

    Je souhaite trouver une fonction qui pourrait s'adapter à ces formes de courbures (cf figure ci-après). J'ai essayé quelques fonctions, notamment la sigmoïde ou une loi de puissance mais ça marche pas dans tous les cas.

    Je suis ouvert à toute suggestion!

    N'hésitez pas si besoin de plus d'informations.

    Nota: Les data numérique sont en bas. La première colonne correspond à X, les autres aux Y

    Cordialement,

    0.090909091 0.691540823 0.025497879 2.00764E-05 1.54129E-09 1.86426E-14
    0.166666667 0.842728138 0.185125646 0.007747254 0.000136812 2.69781E-08
    0.230769231 0.901165535 0.360141625 0.054096448 0.00508921 2.23916E-06
    0.285714286 0.930649458 0.494557362 0.134559505 0.026149239 1.80444E-05
    0.333333333 0.947654916 0.590537642 0.222472105 0.063649994 6.13719E-05
    0.375 0.958379216 0.659105767 0.303157235 0.110019662 0.000139683
    0.411764706 0.965624982 0.709322309 0.372724644 0.158856577 0.000255543
    0.444444444 0.970794234 0.74721452 0.431583793 0.206563487 0.000409384
    0.473684211 0.974644497 0.776625019 0.481303194 0.251475545 0.000600852
    0.5 0.977612816 0.800024432 0.523523047 0.292985144 0.000829319
    0.523809524 0.979965865 0.819040641 0.559654211 0.331011749 0.001094085
    0.545454545 0.981874289 0.834777053 0.590836765 0.365718866 0.001394441
    0.565217391 0.983451783 0.84800259 0.61797295 0.397369839 0.001729695
    0.583333333 0.984776746 0.859266972 0.641773804 0.42625649 0.00209918
    0.6 0.985904856 0.868972394 0.662801498 0.452665127 0.002502258
    0.615384615 0.986876677 0.877419259 0.681503447 0.476861549 0.002938312
    0.62962963 0.987722421 0.884836118 0.69823862 0.499085616 0.003406748
    0.642857143 0.98846503 0.891399744 0.713297493 0.519550496 0.003906994
    0.655172414 0.989122227 0.897248896 0.726917142 0.538444108 0.004438494
    0.666666667 0.989707913 0.90249395 0.739292667 0.555931456 0.005000709
    0.677419355 0.990233139 0.907223758 0.7505859 0.572157217 0.005593118
    0.6875 0.990706797 0.911510626 0.760932089 0.587248267 0.00621521
    0.696969697 0.991136124 0.915413978 0.770445064 0.601315999 0.006866488
    0.705882353 0.991527065 0.918983092 0.779221262 0.614458389 0.007546467
    0.714285714 0.991884549 0.922259166 0.787342894 0.626761806 0.008254672
    0.722222222 0.992212699 0.92527691 0.794880451 0.638302568 0.008990637
    0.72972973 0.992514988 0.928065764 0.801894702 0.64914829 0.009753908
    0.736842105 0.99279436 0.930650867 0.808438309 0.659359035 0.010544034
    0.743589744 0.993053332 0.933053808 0.814557119 0.668988297 0.011360574
    0.75 0.993294063 0.935293232 0.820291232 0.678083851 0.012203093
    0.756097561 0.99351842 0.937385324 0.825675869 0.686688468 0.013071161
    0.761904762 0.993728023 0.939344203 0.830742085 0.694840544 0.013964353
    0.76744186 0.993924283 0.941182237 0.83551737 0.702574629 0.014882249
    0.772727273 0.994108441 0.942910311 0.840026143 0.709921888 0.015824432
    0.777777778 0.994281584 0.944538041 0.844290167 0.716910498 0.016790487
    0.782608696 0.994444676 0.946073949 0.8483289 0.723565994 0.017780004
    0.787234043 0.99459857 0.947525623 0.852159793 0.729911565 0.018792573
    0.791666667 0.994744026 0.948899833 0.855798538 0.735968312 0.019827787
    0.795918367 0.994881722 0.950202643 0.85925929 0.741755482 0.020885241
    0.8 0.995012264 0.9514395 0.862554844 0.747290656 0.021964528
    0.803921569 0.995136199 0.95261531 0.865696799 0.75258993 0.023065247
    0.807692308 0.995254018 0.953734503 0.86869569 0.757668066 0.024186993
    0.811320755 0.995366164 0.95480109 0.871561113 0.762538625 0.025329365
    0.814814815 0.995473039 0.955818712 0.874301822 0.767214085 0.02649196
    0.818181818 0.995575007 0.956790681 0.87692582 0.77170595 0.027674378
    0.821428571 0.995672402 0.957720015 0.879440441 0.776024838 0.028876218
    0.824561404 0.995765524 0.958609474 0.881852417 0.780180567 0.030097079
    0.827586207 0.995854651 0.959461582 0.884167935 0.784182228 0.031336562
    0.830508475 0.995940034 0.960278656 0.886392697 0.788038251 0.03259427
    0.833333333 0.996021908 0.961062823 0.888531961 0.791756462 0.033869802
    0.836065574 0.996100483 0.961816041 0.890590589 0.795344139 0.035162763
    0.838709677 0.996175957 0.962540118 0.892573079 0.798808056 0.036472757
    0.841269841 0.996248511 0.963236721 0.894483598 0.802154527 0.037799389
    0.84375 0.996318312 0.963907392 0.896326018 0.805389445 0.039142266
    0.846153846 0.996385514 0.964553561 0.898103934 0.808518315 0.040500997
    0.848484848 0.996450261 0.965176554 0.899820695 0.811546285 0.041875191
    0.850746269 0.996512685 0.965777602 0.901479419 0.814478176 0.043264461
    0.852941176 0.99657291 0.966357852 0.903083016 0.817318509 0.044668422
    0.855072464 0.99663105 0.966918369 0.904634205 0.820071521 0.046086691
    0.857142857 0.996687213 0.96746015 0.906135529 0.822741197 0.047518887
    0.85915493 0.996741499 0.967984124 0.907589367 0.825331279 0.048964632
    0.861111111 0.996794 0.96849116 0.90899795 0.827845289 0.050423552
    0.863013699 0.996844803 0.968982069 0.910363371 0.830286546 0.051895275
    0.864864865 0.99689399 0.969457615 0.911687596 0.832658178 0.053379433
    0.866666667 0.996941638 0.969918511 0.912972471 0.834963134 0.054875661
    0.868421053 0.996987817 0.970365428 0.914219736 0.8372042 0.056383597
    0.87012987 0.997032595 0.970798996 0.915431027 0.839384011 0.057902885
    0.871794872 0.997076036 0.971219807 0.916607889 0.841505055 0.059433171
    0.873417722 0.997118198 0.971628421 0.917751777 0.84356969 0.060974105
    0.875 0.997159138 0.972025362 0.918864067 0.845580147 0.062525342
    0.87654321 0.997198908 0.972411127 0.919946057 0.847538543 0.064086542
    0.87804878 0.997237558 0.972786185 0.920998977 0.849446885 0.065657367
    0.879518072 0.997275135 0.973150976 0.922023991 0.851307077 0.067237487
    0.880952381 0.997311683 0.973505921 0.923022199 0.853120929 0.068826572
    0.882352941 0.997347244 0.973851414 0.923994646 0.85489016 0.0704243
    0.88372093 0.997381859 0.974187831 0.924942324 0.856616407 0.072030354
    0.885057471 0.997415563 0.974515527 0.925866171 0.858301225 0.07364442
    0.886363636 0.997448394 0.974834838 0.926767083 0.859946097 0.075266189
    0.887640449 0.997480384 0.975146084 0.927645907 0.861552435 0.076895358
    0.888888889 0.997511566 0.975449569 0.928503451 0.863121585 0.078531628
    0.89010989 0.99754197 0.975745581 0.929340484 0.86465483 0.080174706
    0.891304348 0.997571626 0.976034395 0.930157738 0.866153397 0.081824303
    0.892473118 0.99760056 0.976316272 0.930955909 0.867618456 0.083480135
    0.893617021 0.997628798 0.97659146 0.931735664 0.869051124 0.085141923
    0.894736842 0.997656367 0.976860196 0.932497636 0.870452471 0.086809394
    0.895833333 0.997683289 0.977122706 0.933242431 0.871823519 0.08848228
    0.896907216 0.997709587 0.977379205 0.933970626 0.873165246 0.090160315
    0.897959184 0.997735283 0.977629898 0.934682774 0.874478588 0.091843242
    0.898989899 0.997760397 0.977874982 0.935379404 0.875764442 0.093530808
    0.9 0.997784948 0.978114644 0.93606102 0.877023667 0.095222762
    0.900990099 0.997808957 0.978349063 0.936728106 0.878257087 0.096918862
    0.901960784 0.99783244 0.97857841 0.937381124 0.879465493 0.098618869
    0.902912621 0.997855415 0.97880285 0.938020517 0.880649642 0.100322548
    0.903846154 0.997877898 0.979022538 0.938646712 0.881810261 0.10202967
    0.904761905 0.997899905 0.979237626 0.939260114 0.882948051 0.103740011
    0.905660377 0.997921451 0.979448257 0.939861114 0.884063682 0.105453351
    0.906542056 0.99794255 0.979654569 0.940450088 0.885157799 0.107169475
    0.907407407 0.997963217 0.979856695 0.941027394 0.886231022 0.108888173
    0.908256881 0.997983464 0.980054761 0.94159338 0.887283949 0.110609239
    0.909090909 0.998003304 0.98024889 0.942148375 0.888317153 0.112332472
    0.90990991 0.99802275 0.980439198 0.942692701 0.889331187 0.114057674
    0.910714286 0.998041813 0.980625799 0.943226663 0.890326583 0.115784655
    0.911504425 0.998060504 0.980808799 0.943750557 0.891303854 0.117513225
    0.912280702 0.998078834 0.980988302 0.944264667 0.892263493 0.119243202
    0.913043478 0.998096815 0.98116441 0.944769265 0.893205976 0.120974406
    0.913793103 0.998114455 0.981337217 0.945264617 0.894131762 0.122706662
    0.914529915 0.998131764 0.981506817 0.945750974 0.895041295 0.124439799
    0.915254237 0.998148752 0.981673298 0.946228581 0.895935001 0.126173651
    0.915966387 0.998165427 0.981836746 0.946697675 0.896813292 0.127908053
    0.916666667 0.998181799 0.981997244 0.947158482 0.897676566 0.129642848
    0.923076923 0.998330484 0.983456178 0.95135544 0.905561927 0.146980126
    0.933333333 0.998564142 0.985753593 0.957994537 0.918119784 0.181225171
    0.941176471 0.998739512 0.98748171 0.963012832 0.927680608 0.214332601
    0.947368421 0.998876076 0.988829701 0.966941871 0.935207664 0.245909839
    0.952380952 0.998985489 0.989911125 0.970103223 0.941290562 0.275779623
    0.956521739 0.999075154 0.990798313 0.972702957 0.946310607 0.30389511
    0.96 0.99915 0.991539543 0.974879279 0.95052542 0.330285676
    0.962962963 0.999213439 0.992168279 0.976728381 0.954115393 0.355023116
    0.965517241 0.999267909 0.99270846 0.978319297 0.957210644 0.378200863
    0.967741935 0.999315195 0.993177663 0.97970287 0.959907415 0.399921397
    0.96969697 0.999356638 0.993589094 0.980917381 0.962278441 0.420288758
    0.971428571 0.999393265 0.993952861 0.981992208 0.964379721 0.439404221
    0.972972973 0.999425874 0.994276842 0.982950277 0.966255078 0.457363938
    0.974358974 0.999455095 0.994567263 0.983809744 0.967939306 0.47425777
    0.975609756 0.999481433 0.994829111 0.984585175 0.969460379 0.49016886
    0.976744186 0.999505298 0.995066431 0.985288393 0.970841054 0.50517363
    0.978723404 0.999546887 0.995480161 0.986515321 0.973252813 0.532737958
    0.979591837 0.999565119 0.995661599 0.987053769 0.974312381 0.545419623
    0.980392157 0.999581915 0.99582877 0.987550089 0.975289669 0.557440093
    0.982142857 0.999618639 0.996194395 0.988636308 0.977430586 0.584905366
    0.983606557 0.999649332 0.996500096 0.989545247 0.979224279 0.609175009
    0.984848485 0.999675375 0.996759564 0.990317253 0.980749318 0.630764311
    0.985915493 0.999697757 0.996982604 0.990981262 0.982062175 0.650086963
    0.986842105 0.999717201 0.997176424 0.991558575 0.983204486 0.66747778
    0.987654321 0.999734255 0.997346444 0.992065222 0.984207639 0.683210005
    0.988372093 0.999749335 0.997496817 0.992513499 0.98509574 0.69750847
    0.989010989 0.999762767 0.997630782 0.992913 0.98588762 0.710559633
    0.989583333 0.99977481 0.9977509 0.993271318 0.9865982 0.722519294
    0.99009901 0.999785669 0.997859224 0.993594546 0.98723946 0.733518561
    0.990990991 0.999804474 0.998046854 0.994154613 0.988351191 0.753063766
    0.991735537 0.999820197 0.998203762 0.994623175 0.989281873 0.769903797
    0.992366412 0.999833543 0.998336959 0.995021074 0.990072619 0.784564451
    0.992907801 0.999845014 0.998451469 0.995363252 0.990752941 0.797443839
    0.993377483 0.999854982 0.998550987 0.995660708 0.991344577 0.808848797
    0.99378882 0.999863726 0.998638291 0.995921715 0.991863895 0.819019556
    0.994152047 0.99987146 0.99871551 0.996152622 0.992323462 0.828146847
    0.994475138 0.999878349 0.998784307 0.996358378 0.992733081 0.836384015
    0.994764398 0.999884526 0.998845994 0.996542902 0.99310052 0.843855737
    0.995024876 0.999890096 0.998901626 0.996709336 0.993432009 0.850664423
    0.995475113 0.999899743 0.998997989 0.996997677 0.994006461 0.862618352
    0.995850622 0.99990781 0.999078574 0.997238862 0.994487121 0.872773748
    0.996168582 0.999914658 0.999146982 0.997443636 0.994895331 0.881509822
    0.996441281 0.999920544 0.999205791 0.997619706 0.995246401 0.889106
    0.996677741 0.999925659 0.999256899 0.99777274 0.995551601 0.895772743
    0.997150997 0.999935932 0.999359545 0.998080154 0.996164859 0.90934855
    0.997506234 0.999943678 0.999436953 0.998312033 0.996627586 0.919753508
    0.997782705 0.999949731 0.999497446 0.998493274 0.996989354 0.927986562
    0.998003992 0.999954593 0.999546044 0.998638895 0.997280081 0.934666197
    0.998185118 0.999958586 0.999585955 0.9987585 0.997518906 0.940195984
    0.998336106 0.999961925 0.999619326 0.998858517 0.997718646 0.944850566
    0.998463902 0.999964758 0.999647651 0.998943414 0.99788821 0.948823392
    0.998573466 0.999967194 0.999671998 0.999016394 0.998033986 0.952254689
    0.998668442 0.99996931 0.999693154 0.999079812 0.998160673 0.955248614
    0.998751561 0.999971166 0.99971171 0.99913544 0.998271806 0.957884162
    0.998824912 0.999972808 0.999728121 0.999184637 0.998370097 0.960222341
    0.998890122 0.99997427 0.999742739 0.999228462 0.998457661 0.962311025
    0.998948475 0.999975581 0.999755844 0.999267753 0.99853617 0.964188311
    0.999000999 0.999976763 0.999767661 0.999303182 0.998606967 0.965884897
    0.999200639 0.999981276 0.999812776 0.99943846 0.998877311 0.972396154
    0.999333777 0.999984306 0.999843069 0.999529298 0.999058872 0.976798278
    0.999428898 0.999986482 0.999864832 0.999594565 0.999189335 0.979976099
    0.99950025 0.999988123 0.999881235 0.999643759 0.999287675 0.982379578
    0.99960016 0.999990433 0.999904335 0.99971304 0.999426182 0.985776633
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    0.9999875 0.999999673 0.999996735 0.999990204 0.999980408 0.999510333
    0.999988889 0.999999709 0.999997091 0.999991272 0.999982544 0.999563721
    0.99999 0.999999738 0.999997376 0.999992129 0.999984258 0.999606544
    0.999995 0.999999867 0.999998672 0.999996015 0.999992031 0.999800793
    0.999996667 0.999999911 0.999999109 0.999997326 0.999994652 0.999866314
    0.9999975 0.999999933 0.999999329 0.999997986 0.999995971 0.999899293
    0.999998 0.999999946 0.999999461 0.999998383 0.999996767 0.999919171
    0.999998333 0.999999955 0.99999955 0.999998649 0.999997299 0.999932469
    0.999998571 0.999999961 0.999999613 0.99999884 0.99999768 0.999941994
    0.99999875 0.999999966 0.999999661 0.999998983 0.999997966 0.999949154
    0.999998889 0.99999997 0.999999698 0.999999095 0.999998189 0.999954734
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    0.99999998 0.999999999 0.999999994 0.999999983 0.999999966 0.999999154
    0.99999999 1 0.999999997 0.999999991 0.999999983 0.999999575
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    helloworld

    Nozio
    • Mathématiques
      23 mai 2022 à 10:52:37

      Salut, qu'est-ce que tu as tenté comme loi de puissance ? Tu pourrais tenter un truc dans ce genre :

      \(y(x) = (x - x_0)^{n/n_0}\)

      où \(x_0,n_0\) sont deux paramètres à déterminer. Tu peux éventuellement rajouter un terme constant supplémentaire.

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      Avez-vous entendu parler de Julia ? Laissez-vous tenter ...

      robun
      • Mathématiques
        23 mai 2022 à 12:10:06

        Je ne pense pas qu'une puissance puisse correspondre, car la dérivée en 0 reste toujours nulle.
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        the physist
        • Mathématiques
          23 mai 2022 à 13:18:44

          Bonjour Nozio, Robun

          Merci pour vos messages.

          @nozio, je vais tester cela, par contre le n dans l'équation est une variable?

          @robun, merci pour cette indication!

          Bien vous,

          -
          Edité par the physist 23 mai 2022 à 13:21:25

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          helloworld

          Fitting data avec une loi de puissance sigmoïde??

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