在正态分布图中用Matplotlib注释四分位数

问题描述

我正在使用一个数据集，到目前为止，我已经制作了带有覆盖正态分布曲线的直方图.具有正态分布曲线的直方图

I'm working with a data-set, so far i have made a histogram with a overlayed normal distribution curve.Histrogram with normal Distribution Curve

我要在此图像中标出四分位数(箱形图供参考).这是我正在使用的代码:

I want to mark out the quartiles as in this image (the box plot is for reference).This is the code i'm working with:

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

depDelay.sort()
plt.hist(depDelay, bins=100, normed=True)
hmean = np.mean(depDelay)
hstd = np.std(depDelay)
pdf = stats.norm.pdf(depDelay, hmean, hstd)
markers = [np.percentile(depDelay,50)]
plt.plot(DepDelay, pdf,'-o',markevery=markers)
plt.title('Distribution of Departure Delay')
plt.xlabel('Departure Delay (in mins)')
plt.ylabel('Frequency')
plt.savefig('depDelayNormDist.png')
plt.show()

如何使用matplotlib绘制相同的内容?

How can i plot the same using matplotlib ?

推荐答案

我尝试了一些复制引用的图像的方法.不知道标记四分位数的确切含义，但是我在pdf处放置了Q1和Q3的标签，并在四分位数之间添加了百分比.

I've tried to replicate the referenced image somewhat. Not sure what precisely you meant by marking the quartiles, but I've put in labels for Q1 and Q3 at the pdf and percentages in between the quartiles.

import numpy as np
import scipy
import pandas as pd
from scipy.stats import norm
import matplotlib.pyplot as plt
from matplotlib.mlab import normpdf

# dummy data
mu = 0
sigma = 1
n_bins = 50
s = np.random.normal(mu, sigma, 1000)

fig, axes = plt.subplots(nrows=2, ncols=1, sharex=True)

#histogram
n, bins, patches = axes[1].hist(s, n_bins, normed=True, alpha=.1, edgecolor='black' )
pdf = 1/(sigma*np.sqrt(2*np.pi))*np.exp(-(bins-mu)**2/(2*sigma**2))

median, q1, q3 = np.percentile(s, 50), np.percentile(s, 25), np.percentile(s, 75)
print(q1, median, q3)

#probability density function
axes[1].plot(bins, pdf, color='orange', alpha=.6)

#to ensure pdf and bins line up to use fill_between.
bins_1 = bins[(bins >= q1-1.5*(q3-q1)) & (bins <= q1)] # to ensure fill starts from Q1-1.5*IQR
bins_2 = bins[(bins <= q3+1.5*(q3-q1)) & (bins >= q3)]
pdf_1 = pdf[:int(len(pdf)/2)]
pdf_2 = pdf[int(len(pdf)/2):]
pdf_1 = pdf_1[(pdf_1 >= norm(mu,sigma).pdf(q1-1.5*(q3-q1))) & (pdf_1 <= norm(mu,sigma).pdf(q1))]
pdf_2 = pdf_2[(pdf_2 >= norm(mu,sigma).pdf(q3+1.5*(q3-q1))) & (pdf_2 <= norm(mu,sigma).pdf(q3))]

#fill from Q1-1.5*IQR to Q1 and Q3 to Q3+1.5*IQR
axes[1].fill_between(bins_1, pdf_1, 0, alpha=.6, color='orange')
axes[1].fill_between(bins_2, pdf_2, 0, alpha=.6, color='orange')

print(norm(mu, sigma).cdf(median))
print(norm(mu, sigma).pdf(median))

#add text to bottom graph.
axes[1].annotate("{:.1f}%".format(100*norm(mu, sigma).cdf(q1)), xy=((q1-1.5*(q3-q1)+q1)/2, 0), ha='center')
axes[1].annotate("{:.1f}%".format(100*(norm(mu, sigma).cdf(q3)-norm(mu, sigma).cdf(q1))), xy=(median, 0), ha='center')
axes[1].annotate("{:.1f}%".format(100*(norm(mu, sigma).cdf(q3+1.5*(q3-q1)-q3)-norm(mu, sigma).cdf(q3))), xy=((q3+1.5*(q3-q1)+q3)/2, 0), ha='center')
axes[1].annotate('q1', xy=(q1, norm(mu, sigma).pdf(q1)), ha='center')
axes[1].annotate('q3', xy=(q3, norm(mu, sigma).pdf(q3)), ha='center')

axes[1].set_ylabel('probability')

#top boxplot
axes[0].boxplot(s, 0, 'gD', vert=False)
axes[0].axvline(median, color='orange', alpha=.6, linewidth=.5)
axes[0].axis('off')

plt.subplots_adjust(hspace=0)
plt.show()

仅供参考，我已经回答也是一个类似的问题.

FYI, I've answered this similar question as well.

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