如何使用概率密度函数创建相等的条带宽度和相等的条带高度直方图

Humair Ali Palh

通过生成一些随机数据，使用直方图估计概率密度函数。我现在想要直方图的两个版本，即相等的箱宽和相等的箱高直方图。

# -*- coding: utf-8 -*-
from scipy.stats import norm
import matplotlib.pyplot as plt
#import pandas as pd
import numpy as np
fig, ax = plt.subplots(1, 1)

#Calculate a few first moments:
mean, var, skew, kurt = norm.stats(moments='mvsk')

#Display the probability density function (pdf):
x = np.linspace(norm.ppf(0.01),
                norm.ppf(0.99), 100)
ax.plot(x, norm.pdf(x),
       'r-', lw=5, alpha=0.6, label='norm pdf')

#Freeze the distribution and display the frozen pdf:
rv = norm()
ax.plot(x, rv.pdf(x), 'b-', lw=2, label='frozen pdf')

#Check accuracy of cdf and ppf:
vals = norm.ppf([0.001, 0.5, 0.999])
np.allclose([0.001, 0.5, 0.999], norm.cdf(vals))

#Generate random numbers:
r = norm.rvs(size=10000)

#df = pd.read_excel('ardata.xlsx')
#r = df[['dest','source']].values


#And compare the histogram:
ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
ax.legend(loc='best', frameon=False)
plt.show()

Panadestein

如果要生成具有相同宽度和高度的直方图，则不能使用正态分布的随机样本（请参见rvs函数的文档）。为了实现期望的目标，您需要从分布中获取确定性样本。您可以例如：

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm


fig, ax = plt.subplots(1, 1)

# Display the probability density function (pdf):

xppf = np.linspace(norm.ppf(0.01),
                   norm.ppf(0.99), 100000)

ax.plot(xppf, norm.pdf(xppf, loc=0),
        'r-', lw=3, alpha=0.6, label='norm pdf')

# Create histogram:

mybins = np.linspace(norm.ppf(0.01), norm.ppf(0.99), num=12)  # Evenly spaced bins
myvals = np.linspace(0.01, 0.99, 100000)

ax.hist(norm.ppf(myvals, loc=0), bins=mybins, density=True,
        histtype='stepfilled', alpha=0.2)

ax.legend(loc='best', frameon=False)
plt.xlabel(r'x')
plt.ylabel(r'PDF(x)')
plt.show()

哪些情节：