Python 使用matplotlib按样本绘制概率密度函数
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Plotting probability density function by sample with matplotlib
提问by Cupitor
I want to plot an approximation of probability density function based on a sample that I have; The curve that mimics the histogram behaviour. I can have samples as big as I want.
我想根据我拥有的样本绘制概率密度函数的近似值；模仿直方图行为的曲线。我可以拥有任意大的样品。
采纳答案by askewchan
If you want to plot a distribution, and you know it, define it as a function, and plot it as so:
如果您想绘制分布并且您知道它，请将其定义为函数，并按如下方式绘制：
import numpy as np
from matplotlib import pyplot as plt
def my_dist(x):
return np.exp(-x ** 2)
x = np.arange(-100, 100)
p = my_dist(x)
plt.plot(x, p)
plt.show()
If you don't have the exact distribution as an analytical function, perhaps you can generate a large sample, take a histogram and somehow smooth the data:
如果您没有作为分析函数的精确分布，也许您可以生成一个大样本，获取直方图并以某种方式平滑数据：
import numpy as np
from scipy.interpolate import UnivariateSpline
from matplotlib import pyplot as plt
N = 1000
n = N//10
s = np.random.normal(size=N) # generate your data sample with N elements
p, x = np.histogram(s, bins=n) # bin it into n = N//10 bins
x = x[:-1] + (x[1] - x[0])/2 # convert bin edges to centers
f = UnivariateSpline(x, p, s=n)
plt.plot(x, f(x))
plt.show()
You can increase or decrease s(smoothing factor) within the UnivariateSplinefunction call to increase or decrease smoothing. For example, using the two you get:
您可以s在UnivariateSpline函数调用中增加或减少（平滑因子）以增加或减少平滑。例如，使用你得到的两个：
回答by EnricoGiampieri
What you have to do is to use the gaussian_kde from the scipy.stats.kde package.
您需要做的是使用 scipy.stats.kde 包中的 gaussian_kde。
given your data you can do something like this:
鉴于您的数据，您可以执行以下操作：
from scipy.stats.kde import gaussian_kde
from numpy import linspace
# create fake data
data = randn(1000)
# this create the kernel, given an array it will estimate the probability over that values
kde = gaussian_kde( data )
# these are the values over wich your kernel will be evaluated
dist_space = linspace( min(data), max(data), 100 )
# plot the results
plt.plot( dist_space, kde(dist_space) )
The kernel density can be configured at will and can handle N-dimensional data with ease. It will also avoid the spline distorsion that you can see in the plot given by askewchan.
核密度可以随意配置，可以轻松处理N维数据。它还将避免您在 askewchan 给出的图中看到的样条扭曲。
