How to locate the median in a KDE plot

Question

I am trying to do a Kernel Density Estimation (KDE) plot with seaborn and locate the median. The code looks something like this:

import seaborn as sns
import numpy as np
import matplotlib.pyplot as plt

sns.set_palette("hls", 1)
data = np.random.randn(30)
sns.kdeplot(data, shade=True)

# x_median, y_median = magic_function()
# plt.vlines(x_median, 0, y_median)

plt.show()

As you can see I need a magic_function() to fetch the median x and y values from the kdeplot. Then I would like to plot them with e.g. vlines. However, I can't figure out how to do that. The result should look something like this (obviously the black median bar is wrong here):

I guess my question is not strictly related to seaborn and also applies to other kinds of matplotlib plots. Any ideas are greatly appreciated.

Gyrostatic

Answer 1

You need to:

1. Extract the data of the kde line
2. Integrate it to calculate the cumulative distribution function (CDF)
3. Find the value that makes CDF equal 1/2, that is the median

import numpy as np
import scipy
import seaborn as sns
import matplotlib.pyplot as plt

sns.set_palette("hls", 1)
data = np.random.randn(30)
p=sns.kdeplot(data, shade=True)

x,y = p.get_lines()[0].get_data()

#care with the order, it is first y
#initial fills a 0 so the result has same length than x
cdf = scipy.integrate.cumtrapz(y, x, initial=0)

nearest_05 = np.abs(cdf-0.5).argmin()

x_median = x[nearest_05]
y_median = y[nearest_05]

plt.vlines(x_median, 0, y_median)
plt.show()

Empson

It's scipy.integrate.cumulative_trapezoid now. – Menchaca