MATLAB: Curve Fitting Weibull error

Question

Hello,

I am trying to find the corresponding parameters for my model function.

I always get this error message :

Error using internal.stats.getscheffeparam>ValidateParameters (line 182)

If non-empty, JW must be a numeric, real matrix.

This is the correspnding code :

x0 is the initial estimation of the 3 parameters P(1) P(2) P(3)

xdata = [0:660];
ydata = [1.022608794,1.009868918,1.009812254,1.001822681,0.995703007,0.995910774,0.991103808,0.993474237,0.991292687,0.996392415,0.996184648,0.9975068,0.995665231,1.000103883,1.002077667,1.001992672,1.002257102,0.995627455,0.988978921,0.989876095,0.993294802,0.991472121,0.989951647,0.993209807,0.997062934,0.98818563,0.997270701,0.999338924,0.994050317,0.990574947,1.001926564,1.000944394,1.012919311,1.020691674,1.020616123,1.01528974,1.016158583,1.007857359,1.006563539,1.00512806,1.01346706,1.002427093,0.999631686,1.000349426,1.000613856,0.993020928,0.990886597,0.989290571,0.985343004,0.983491992,0.986051299,0.995041931,0.99621298,0.993738667,0.995750227,1.001492143,1.000897174,1.00579858,1.016366349,1.019067316,1.008121789,1.006138561,0.996297975,0.985522439,0.978005062,0.982462602,0.979374433,0.993105923,0.994446963,0.997204594,0.994163645,0.996090209,0.982538154,0.985305228,0.991689332,0.997610683,1.00668631,1.011134406,1.013939257,1.008905636,1.010331671,1.000736627,1.001086053,0.999896117,0.995976881,0.989271683,0.991424902,0.988572832,0.989073361,0.988062859,0.987486778,0.990376624,0.995693563,0.993700892,0.999395588,1.004202554,1.005562481,1.003314823,0.99710071,1.00517528,1.012758764,1.004325325,1.007602372,1.022816561,1.015195301,1.010001133,1.020351692,1.022127153,1.021296086,1.029181777,1.049958447,1.075853732,1.126633802,1.184978468,1.269520626,1.352089,1.448313312,1.54306437,1.649025385,1.723736401,1.798116878,1.856149894,1.906108341,1.949021608,1.975445754,1.975880175,1.967493956,1.920425355,1.851900121,1.789012919,1.73890337,1.679236552,1.635813312,1.600407978,1.578696358,1.551563917,1.539428453,1.528596253,1.515365292,1.503324267,1.496751284,1.479837186,1.460590435,1.449843231,1.429982623,1.413899592,1.404767301,1.404417875,1.390790269,1.391866878,1.381591871,1.378550922,1.375831067,1.369343079,1.364819432,1.353231717,1.340992369,1.32654314,1.322680568,1.320338471,1.324729903,1.321840057,1.321027879,1.316126473,1.3035377,1.29244107,1.290108416,1.285112572,1.285773648,1.281854412,1.28347877,1.281656089,1.279257328,1.268444016,1.269709504,1.262919311,1.258169009,1.253711469,1.263287625,1.256884633,1.247742898,1.23849728,1.235682986,1.225256875,1.219892717,1.232604261,1.232396494,1.224161378,1.221469855,1.212620882,1.201108719,1.198492747,1.205273497,1.208201118,1.208758311,1.204839075,1.207048957,1.202251435,1.194091871,1.195574569,1.200409867,1.197538909,1.192949154,1.195177924,1.190002644,1.191249244,1.191475899,1.195716228,1.188094968,1.18941712,1.185563992,1.177744409,1.171841946,1.165344515,1.159205953,1.152614083,1.150375869,1.145266697,1.147986552,1.143736778,1.141668555,1.138183741,1.138249849,1.130590813,1.129674751,1.119191976,1.116424902,1.113110079,1.116661,1.116594893,1.112071245,1.113053415,1.109105848,1.112996751,1.113393397,1.114904427,1.112600106,1.116160471,1.116151028,1.110824645,1.112656769,1.118124811,1.119333636,1.110701874,1.11670822,1.120211922,1.11225068,1.103505591,1.104110003,1.102051224,1.097725899,1.104062783,1.100615745,1.101843457,1.096583182,1.09700816,1.088423617,1.099520248,1.093853883,1.091898988,1.100691296,1.110210789,1.102362874,1.099964113,1.099784678,1.097338697,1.085647099,1.087224237,1.09027463,1.091030145,1.080075174,1.084551602,1.074711015,1.068355243,1.066929208,1.072057268,1.068100257,1.076939785,1.072586129,1.076713131,1.067996374,1.068638561,1.06820414,1.075693185,1.069044651,1.074711015,1.073039438,1.073445527,1.071688954,1.071887277,1.073247205,1.071027879,1.065361514,1.073369976,1.069346857,1.064908205,1.064388788,1.058967966,1.055842022,1.060998413,1.058457993,1.056625869,1.061583938,1.061555606,1.053197718,1.056219779,1.053188274,1.051639468,1.04618087,1.052385539,1.047814672,1.045718117,1.0402123,1.038899592,1.036217513,1.042592173,1.049580689,1.058023572,1.064870429,1.067646948,1.063321623,1.055417044,1.049977335,1.044896494,1.049117936,1.044820943,1.044839831,1.052224992,1.052121109,1.047890224,1.054349879,1.058854639,1.055709807,1.048759066,1.047323587,1.042582729,1.045727561,1.043262693,1.047181928,1.043196585,1.041893321,1.03788909,1.037501889,1.032751587,1.0293801,1.020427244,1.026754684,1.03026783,1.04078838,1.048749622,1.05928906,1.049967891,1.052942732,1.041610003,1.046105319,1.040731717,1.042932155,1.036963584,1.048466304,1.037161907,1.044112647,1.04555757,1.040693941,1.03343155,1.036123073,1.037596328,1.03918291,1.041949985,1.040098972,1.038956256,1.034017075,1.034224841,1.036368616,1.044320414,1.054444319,1.050883953,1.047333031,1.036311952,1.027226881,1.02068223,1.026565805,1.026376927,1.031051677,1.027972953,1.033337111,1.027330765,1.030758915,1.029568979,1.031278332,1.025914173,1.029313992,1.022221593,1.026934119,1.02746298,1.029276216,1.034300393,1.042337186,1.037549108,1.037690768,1.033261559,1.02746298,1.022419915,1.029049562,1.032553264,1.031523874,1.039031807,1.032789362,1.031438879,1.031958296,1.030541704,1.024620354,1.022948776,1.019029541,1.011361061,1.014723104,1.012003249,1.023373753,1.029833409,1.032024403,1.032609927,1.031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fun = @(P,x)(-P(1)/P(2)).*(((x-P(3))/P(2)).^(P(1)-1)).*exp(-((x-P(3))/n).^P(1));
x0=[-1.2,33.15,105];
g = fitnlm(xdata,ydata,fun,x0)

Answer 1

We are given not much more than this:

fun = @(P,x)(-P(1)/P(2)).*(((x-P(3))/P(2)).^(P(1)-1)).*exp(-((x-P(3))/n).^P(1));

fun is a function of P and x. But then we see the number n. No hint as to what n is.

I might guess 17, or some others might guess 42, which is probably the answer to all questions in the end anyway.

So, is n a typo? If not, and n has some reasonable value that you have kept secret, there are still issues. I cannot test your code, since there is no hint about n. But something in your code is producing results that are not real numbers. I looked at ydata, and it is all real.

But consider code fragments like this:

(((x-P(3))/P(2)).^(P(1)-1))

x is a vector of integers. We see that as the vector: 0:660.

We have x0 as:

x0=[-1.2,33.15,105];

So P(3) is 105, although as iterations proceed, it will not remain an integer. Anyway, if we take the vector [0:660], then subtract something on the order of 105 from it, we will have some arbitrary negative numbers.

ANd P(1) is something on the order of -1.2. So we then raise those numbers with various signs on them to some non-integer power. Just for kicks, what is this:

(-105)^-1.2
ans =
       -0.00303759931155025 +   0.00220694508288106i

Oh, yes. Raising a negative number to some real, non-integer power produces complex numbers. If I now read the error message, I start to wonder if this is what produces the error. In turn, that brings about some questions as to the validity of your model, or possibly about the parameters you have chosen as start points.