指数Weibull分布上的Curve_fit失败

Question

我试着用

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

为了确定指数威布尔分布的参数：

#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 )

然后发生错误：

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

我不知道哪一步有问题，有人能帮忙吗？

谢谢

Answer 1

在这里阅读curve_fit方法的文档，fit.html，关于方法参数，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，阅读返回值部分中关于“pcov”的内容时，他们提到如果是the Jacobian matrix at the solution does not have a full rank，条目将是inf。

我用trf和dogbox尝试了您的代码，得到了充满零的pconv数组。