使用matplotlib通过样本绘制概率密度函数

Question

我想根据我的样本绘制概率密度函数的近似值; 模拟直方图行为的曲线.我可以提供我想要的样品.

Answer 1

如果要绘制分布,并且知道它,请将其定义为函数,并将其绘制为:

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()

如果您没有确切的分布作为分析函数,也许您可​​以生成一个大样本,采用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()

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,使用这两个:

Answer 2

你要做的是使用scipy.stats.kde包中的gaussian_kde.

根据您的数据,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) )

内核密度可以随意配置,并且可以轻松处理N维数据.它还可以避免你在askewchan给出的图中看到的样条扭曲.