pandas 用python拟合直方图
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Histogram fitting with python
提问by user2820579
I've been surfing but haven't found the correct method to do the following.
我一直在冲浪，但还没有找到执行以下操作的正确方法。
I have a histogram done with matplotlib:
我有一个用 matplotlib 做的直方图：
hist, bins, patches = plt.hist(distance, bins=100, normed='True')
From the plot, I can see that the distribution is more or less an exponential (Poisson distribution). How can I do the best fitting, taking into account my hist and bins arrays?
从图中，我可以看到分布或多或少是指数分布（泊松分布）。考虑到我的 hist 和 bins 数组，我该如何做最好的拟合？
UPDATE
更新
I am using the following approach:
我正在使用以下方法：
x = np.float64(bins) # Had some troubles with data types float128 and float64
hist = np.float64(hist)
myexp=lambda x,l,A:A*np.exp(-l*x)
popt,pcov=opt.curve_fit(myexp,(x[1:]+x[:-1])/2,hist)
But I get
但我得到
---> 41 plt.plot(stats.expon.pdf(np.arange(len(hist)),popt),'-')
ValueError: operands could not be broadcast together with shapes (100,) (2,)
回答by CT Zhu
What you described is a form of exponential distribution, and you want to estimate the parameters of the exponential distribution, given the probability density observed in your data. Instead of using non-linear regression method (which assumes the residue errors are Gaussian distributed), one correct way is arguably a MLE (maximum likelihood estimation).
您所描述的是一种形式的指数分布，并且您希望根据数据中观察到的概率密度来估计指数分布的参数。而不是使用非线性回归方法（假设残差是高斯分布的），一种正确的方法可以说是 MLE（最大似然估计）。
scipyprovides a large number of continuous distributions in its statslibrary, and the MLE is implemented with the .fit()method. Of course, exponential distribution is there:
scipy在其stats库中提供了大量的连续分布，MLE 是用该.fit()方法实现的。当然，指数分布是存在的：
In [1]:
import numpy as np
import scipy.stats as ss
import matplotlib.pyplot as plt
%matplotlib inline
In [2]:
#generate data
X = ss.expon.rvs(loc=0.5, scale=1.2, size=1000)
#MLE
P = ss.expon.fit(X)
print P
(0.50046056920696858, 1.1442947648425439)
#not exactly 0.5 and 1.2, due to being a finite sample
In [3]:
#plotting
rX = np.linspace(0,10, 100)
rP = ss.expon.pdf(rX, *P)
#Yup, just unpack P with *P, instead of scale=XX and shape=XX, etc.
In [4]:
#need to plot the normalized histogram with `normed=True`
plt.hist(X, normed=True)
plt.plot(rX, rP)
Out[4]:
Your distancewill replace Xhere.
您distance将X在这里更换。
