Matplotlib - cumulative density plot with Y-axis as cumulative fraction

Question

I can make a cumulative density plot ( cumulative distribution plots python ):

import numpy as np
import matplotlib.pyplot as plt

# Some fake data:
data = np.random.randn(1000)

sorted_data = np.sort(data)  # Or data.sort(), if data can be modified

# Cumulative counts:
plt.step(np.concatenate([sorted_data, sorted_data[[-1]]]),
         np.arange(sorted_data.size+1))

plt.show()

However, I would like the Y-axis to be represented as the cumulative fraction. Some value between 0 and 1. How can I scale my Y-axis to do this?

Solution

See answer by Ernest below. If using Python 2:

plt.step(np.concatenate([sorted_data, sorted_data[[-1]]]), np.arange(sorted_data.size+1)/float(sorted_data.size))

Answer 1

Not to overly complicate things, just divide by the number of data you have

import numpy as np
import matplotlib.pyplot as plt

# Some fake data:
data = np.random.randn(1000)

sorted_data = np.sort(data)  # Or data.sort(), if data can be modified

# Cumulative counts:
plt.step(np.concatenate([sorted_data, sorted_data[[-1]]]),
         np.arange(sorted_data.size+1)/sorted_data.size)

plt.show()

Answer 2

In general, you could use min-max scaling by subtracting your values from the minimum and dividing by the difference between the max and min values.

y = np.arange(sorted_data.size+1)
# Using min-max scaling
y = (y - np.min(y)) / (np.max(y) - np.min(y))

Since the minimum of y in this case is 0, that's the same as dividing by the maximum of your y-values.

plt.step(np.concatenate([sorted_data, sorted_data[[-1]]]),
     y / np.max(y))