0

私はこのデータセットを持っています:

X:              Y:       
0.          0.
0.001417162 0.0118
0.002352761 0.0128
0.003123252 0.0135
0.003866221 0.0138
0.004045083 0.0147
0.005544762 0.0151
0.006260197 0.0156
0.007195755 0.0157
0.007883656 0.0158
0.008805432 0.0159
0.009314465 0.0165
0.010566391 0.0168
0.011047891 0.0186
0.011666955 0.0177
0.012341036 0.0225
0.013193938 0.0399
0.013854235 0.087
0.014500764 0.1479
0.015381122 0.198
0.015601208 0.2586
0.01638525  0.3111
0.016976706 0.3693
0.017691939 0.42
0.018338382 0.4737
0.018861027 0.5223
0.01963122  0.5691
0.021625353 0.6183
0.020923988 0.6684
0.021377815 0.711
0.021927895 0.7551
0.022574222 0.7938
0.023633053 0.8382
0.023646804 0.8742
0.024279325 0.912
0.025131822 0.9495
0.0256543   0.9891
0.026094271 1.0215
0.026685464 1.0596
0.027345378 1.098
0.028101497 1.1328
0.028513912 1.1739
0.029077528 1.1997
0.029723601 1.2339
0.030355902 1.2741
0.031056901 1.3041
0.031428005 1.3383
0.032087723 1.3665
0.032692438 1.3983
0.033242157 1.4262
0.033846824 1.4589
0.034410239 1.4877
0.035248448 1.5222
0.035729364 1.5534
0.036430096 1.5861
0.037034618 1.6179
0.037694064 1.6536
0.038408425 1.6842
0.039067798 1.7121
0.039521096 1.7427
0.040207877 1.7763
0.04071607  1.8075
0.041279177 1.8381
0.04129291  1.8711
0.042707418 1.9065
0.043366544 1.9332
0.043860863 1.9659
0.044368889 1.9959
0.045055371 2.0202
0.045700624 2.0487
0.04626347  2.0796
0.047059639 2.1105
0.047540055 2.1339
0.048308673 2.1618
0.048857648 2.1849
0.049557546 2.2203
0.050229948 2.2425
0.052082233 2.2716
0.051355084 2.2983
0.051945039 2.3193
0.052466363 2.3475
0.053371748 2.3718
0.053851839 2.3937
0.054647359 2.4189
0.055072521 2.4372
0.055675941 2.4633
0.056306742 2.4882
0.057060898 2.5131
0.057691594 2.5332
0.058582712 2.5527
0.059007671 2.5755
0.059597094 2.5941
0.060172767 2.6115
0.065187502 2.6403
0.06131028  2.6592
0.061968042 2.6808
0.062598344 2.6991
0.063173791 2.7246
0.063790292 2.7441
0.064393043 2.7633
0.065091624 2.7795
0.065502522 2.8011
0.066433804 2.8212
0.066598135 2.8368
0.067351271 2.8545
0.067981104 2.8665
0.068610879 2.8845
0.069309041 2.9046
0.069870256 2.9214
0.070253498 2.9355
0.070828319 2.9499
0.07159467  2.9691
0.072046228 2.9856
0.072620893 2.9982
0.07326391  3.0108
0.073893183 3.0255
0.074467682 3.0387
0.075165218 3.0531
0.075862676 3.0654
0.076395973 3.0735
0.077230012 3.0879
0.077571798 3.0996
0.077968246 3.1116
0.078720058 3.1251
0.079485442 3.1332
0.080168736 3.1473
0.080797297 3.1524
0.081671703 3.1647
0.082518656 3.1761
0.082737205 3.1794
0.083242565 3.1911
0.083843476 3.207
0.084594523 3.2157
0.083993693 3.2217
0.086028058 3.2313
0.086806105 3.2412
0.087515804 3.2475
0.087979788 3.2562
0.089221428 3.2658
0.089289641 3.2727
0.090053572 3.2823
0.090599168 3.285
0.091485638 3.2988
0.092508299 3.3006
0.092794607 3.309
0.093585278 3.3177
0.094443969 3.3255
0.095029975 3.336
0.095752165 3.3381
0.096378886 3.3468
0.097182604 3.3498
0.097781901 3.3573
0.098585385 3.3612
0.099238967 3.3702
0.102192566 3.372
0.100464189 3.3816
0.101226388 3.3879
0.101961246 3.396
0.102519116 3.4038
0.103335387 3.4113
0.103920292 3.4134
0.104777107 3.4206
0.105416212 3.423
0.105932869 3.4308
0.106952407 3.4353
0.107550426 3.4431
0.108284246 3.4479
0.108759804 3.4539
0.109439081 3.4587
0.110118251 3.4662
0.11096027  3.4701
0.111802122 3.4749
0.112182257 3.4857
0.113132445 3.4902
0.113878868 3.4929
0.114530181 3.5028
0.11465229  3.5076
0.116063069 3.513
0.116619106 3.5181
0.117378448 3.5247
0.118246089 3.5295
0.118869589 3.5286
0.119479439 3.5364
0.120292424 3.5451
0.120807227 3.5511
0.121728283 3.5565
0.122283519 3.5625
0.123068837 3.5622
0.123745705 3.5691
0.124544254 3.5775
0.125247919 3.5796
0.125924395 3.5868
0.126614273 3.5892
0.128683133 3.5958
0.127993643 3.5991
0.128602023 3.6057
0.129507645 3.6093
0.130115772 3.6132
0.130669753 3.6156
0.131682911 3.6222
0.132263658 3.6234
0.132911821 3.6288
0.133870342 3.6291
0.136717348 3.6336
0.13504451  3.6396
0.135692157 3.6372
0.13621828  3.6432
0.137068001 3.6465
0.141030546 3.6522
0.138470251 3.6501
0.139009423 3.6567
0.140181824 3.6615
0.140532116 3.6633
0.141124835 3.6588
0.141717448 3.6675
0.14257924  3.6711
0.143319661 3.6741
0.143844585 3.6729
0.144813453 3.6753
0.145243967 3.678
0.1472209   3.6849
0.14672342  3.6879
0.147301565 3.6888
0.147866163 3.6933
0.148403782 3.6927
0.149277216 3.6972
0.149962355 3.7011
0.151922897 3.7077
0.151426165 3.7023
0.152070559 3.7089
0.153251595 3.7107
0.153587034 3.7134
0.15429804  3.7191
0.154861361 3.7191
0.155706144 3.7221
0.157086785 3.7206
0.157086785 3.7272
0.156925966 3.7269
0.158480178 3.7335
0.15912306  3.7272
0.159618519 3.7356
0.160381629 3.7359
0.161171304 3.7386
0.161853731 3.7377
0.162415608 3.7398
0.163151233 3.7437
0.163993625 3.7443
0.165062969 3.7533
0.165330242 3.7509
0.166065112 3.7512
0.166866568 3.7569
0.167494215 3.7635
0.168108371 3.7569
0.168829162 3.7638
0.169536423 3.7626
0.173429745 3.7581
0.171070418 3.7617
0.171803762 3.7653
0.172790131 3.7635
0.172936723 3.7644
0.174029244 3.7695
0.174761783 3.7701
0.175334355 3.7668
0.176173017 3.7704
0.176705362 3.7722
0.177490375 3.7701
0.178261854 3.774
0.178979922 3.7797
0.178793775 3.78
0.180774223 3.7887
0.182394664 3.8301
0.18451827  3.8169
0.186282158 3.8067
0.186772642 3.7731
0.188058046 3.7782
0.188587916 3.7734
0.189395747 3.7749
0.189885613 3.7707
0.190560674 3.7734
0.191447234 3.7752
0.192280569 3.7713
0.193007849 3.7704
0.193946376 3.7701
0.194329613 3.7734
0.195188367 3.7647
0.195716677 3.7644
0.196416507 3.7683
0.197142527 3.7695
0.197709986 3.7596
0.198923623 3.7662
0.199714786 3.7617
0.200189355 3.7626
0.2011382   3.7683
0.201915434 3.7665
0.202310538 3.7599
0.203258508 3.7656
0.204153451 3.7569
0.204903352 3.753
0.205311089 3.7512
0.206192075 3.753
0.207033292 3.7461
0.207966146 3.7539
0.208478393 3.7473
0.209318747 3.7425
0.210119413 3.7455
0.21077548  3.7443
0.21140512  3.7425
0.21234924  3.7443
0.213122589 3.7461
0.213751552 3.7443
0.214498207 3.7422
0.215192234 3.7425
0.216030006 3.7395
0.216762788 3.7437
0.217508397 3.7377
0.218096851 3.7446
0.223098604 3.7383
0.219547672 3.7386
0.220187807 3.7395
0.220906094 3.7386
0.221872127 3.7368
0.222381072 3.7404
0.223111647 3.7374
0.223789808 3.7365
0.224207027 3.7278
0.225288796 3.7359
0.225862032 3.7326
0.226487197 3.7368
0.226396039 3.7302
0.227775995 3.7308
0.228426593 3.7287
0.229115997 3.7278
0.229063975 3.7269
0.230312139 3.726
0.23101389  3.7104

plot(x,y)

モデルの提案を教えてください (私は多項式を試しましたが、フィットが悪いかオーバーフィットのどちらかです)。ありがとう！

4

1 に答える 1

1

Just monkeying around in Python/Numpy for a few minutes, it looks like you want a formula like

Yfit(x) = Ymax * (1 - exp(-(x-x0)/a) )

x0 is where the data starts to take off from zero. Looks like x0 = 0.012 give or take a little. Ymax is the maximum value. The parameter a sets how fast the curve rises, and it look like you want a = 0.007 or so.

Polynomials are bad for any data that levels off and holds steady before or after the interesting parts. Polynomials like to wiggle, like a snake trying to go through lined-up croquet wickets. Even fitting loosely with least-squares or whatever, polynomials don't like flatness. But the shape sure looks like a constant minus a decaying exponential - very common in electronics and physics.

The initial zero values, I take to be meaningless and not needing fitting. The Yfit values you get could be clipped to zero when negative, for plotting and comparison.

If exp(-(x-x0)/a) doesn't work well enough, you could try other functions that quickly fade to zero, such as 1/(1+x^p) for some power p>=2, or use a Gaussian exp(-(x-x0)^2 / a^2)

I actually see a slight curve - the Y values go up to max, and then slightly back down. Maybe add a quadratic term to your model, like:

Y_extra_term(x) = ((x-xmax)/b)^2

where xmax is the x value where y is maximum. (BTW, I'm no expert on R, so use the correct syntax not whatever I write.)

于 2013-06-12T03:33:02.717 に答える