CODEWITHSUNDEEP
pythonscipycurve-fittingweibull
Lin Qiao
Lin Qiao

Reputation: 11

Curve_fit fails on Exponentiated Weibull distribution

I am trying to use

scipy.optimize.curve_fit(func,xdata,ydata)

To determine the parameters of exponentiated weibull distribution:

#define exponentiated weibull distribution
def expweib(x,k,lamda,alpha):
      return alpha*(k/lamda)*((x/lamda)**(k-1))*((1-np.exp(-(x/lamda)*k))**(alpha-1))*np.exp(-(x/lamda)*k)


 #First generate random sample of exponentiated weibull distribution using stats.exponweib.rvs
data = stats.exponweib.rvs(a = 1, c = 82.243021128368554, loc = 0,scale = 989.7422, size = 1000 )


#Then use the sample data to draw a histogram
entries_Test, bin_edges_Test, patches_Test = plt.hist(data, bins=50, range=[909.5,1010.5], normed=True)

#calculate bin middles of the histogram
bin_middles_Test = 0.5*(bin_edges_Test[1:] + bin_edges_Test[:-1])

#use bin_middles_Test as xdata, bin_edges_Test as ydata, previously defined expweib as func, call curve_fit method:
params, pcov = curve_fit(weib,bin_middles_Test, entries_Test )

Then the error occurs:

OptimizeWarning: Covariance of the parameters could not be estimatedcategory=OptimizeWarning)

I cannot identify which step has the issue, could anyone help?

Thank you

Upvotes: 1

Views: 379

Answers (1)

Ankit Paliwal
Ankit Paliwal

Reputation: 156

Reading through documentation for curve_fit method here, https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html, for method argument, they have mentioned that the default 'lm' method won't work if the number of observations is less than the number of variables, in which case you should use either of *'trf'* or *'dogbox'* method.

Also, reading about 'pcov' in Return values section, they have mentioned that the entries will be inf if the Jacobian matrix at the solution does not have a full rank.

I tried your code with both trf and dogbox and got pconv array full of zeros

Upvotes: 1

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