How to plot cdf in Matplotlib in Python?

A Cumulative Distribution Function (CDF) shows the probability that a random variable takes a value less than or equal to a given value. In matplotlib, we can plot a CDF by calculating cumulative probabilities from histogram data.

Steps to Plot CDF

To plot a CDF in matplotlib, follow these steps:

• Generate or prepare your sample data

• Create a histogram to get frequency counts and bin edges

• Calculate the probability density function (PDF) by normalizing counts

• Compute the CDF using cumulative sum of PDF values

• Plot the CDF using matplotlib's plot() method

Example

Here's how to plot a CDF from normally distributed random data:

import numpy as np
import matplotlib.pyplot as plt

# Set figure size
plt.figure(figsize=(8, 5))

# Generate sample data
N = 500
data = np.random.randn(N)

# Create histogram
count, bins_count = np.histogram(data, bins=20)

# Calculate PDF (probability density function)
pdf = count / sum(count)

# Calculate CDF (cumulative distribution function)
cdf = np.cumsum(pdf)

# Plot CDF
plt.plot(bins_count[1:], cdf, marker='o', linestyle='-', label="CDF")
plt.xlabel('Value')
plt.ylabel('Cumulative Probability')
plt.title('Cumulative Distribution Function')
plt.grid(True, alpha=0.3)
plt.legend()
plt.show()

Alternative Method Using scipy.stats

For a smoother CDF, you can use scipy's built-in functions:

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

# Generate sample data
data = np.random.normal(0, 1, 1000)

# Sort data for plotting
sorted_data = np.sort(data)
y_values = np.arange(1, len(sorted_data) + 1) / len(sorted_data)

# Plot empirical CDF
plt.figure(figsize=(8, 5))
plt.plot(sorted_data, y_values, label='Empirical CDF', linewidth=2)
plt.xlabel('Value')
plt.ylabel('Cumulative Probability')
plt.title('Empirical Cumulative Distribution Function')
plt.grid(True, alpha=0.3)
plt.legend()
plt.show()

Key Points

• CDF values range from 0 to 1

• The CDF is always non-decreasing

• More bins in the histogram provide smoother CDF curves

• Use np.cumsum() to calculate cumulative probabilities

Conclusion

Plotting a CDF in matplotlib involves creating a histogram, calculating the PDF, and then computing cumulative probabilities. This visualization helps understand the distribution of your data and probability thresholds.