python - Curve_fit 在指数威 bool 分布上失败

Question

我正在尝试使用

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

确定指数威 bool 分布的参数:

#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 )

然后出现错误:

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

我无法确定哪个步骤有问题，有人可以帮忙吗？

谢谢

Answer 1

在此处阅读 curve_fit 方法的文档，https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html ，对于方法参数，他们提到了 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 .

此外，在“返回值”部分中阅读有关“pcov”的内容，他们提到如果 the Jacobian matrix at the solution does not have a full rank ，则条目将为 inf .

我用 trf 和 dogbox 尝试了你的代码，并得到了全是零的 pconv 数组