Curve_fit在指数威布尔分布上失败

Question

我正在尝试使用

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

要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)

我无法确定哪个步骤有问题，有人可以帮忙吗？

谢谢

Answer 1

在这里阅读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">的信息时，他们提到如果the Jacobian matrix at the solution does not have a full rank，条目将是inf。

我用trf和狗盒尝试了你的代码，得到了充满零的 pconv 数组