Chi-Square Distribution in NumPy

The Chi-Square Distribution is used in statistics when we add up the squares of independent random numbers that follow a standard normal distribution. It is used in hypothesis testing to check whether observed data fits a particular distribution or not. In Python you can use the numpy.random.chisquare() function to generate random numbers that follow Chi-Square Distribution.

Syntax: numpy.random.chisquare(df, size=None)

• df: Degrees of freedom (denoted by k) which affects the shape of the distribution.
• size: The number of random numbers you want to generate or the shape of the returned array.

Example 1: Generate a Single Random Number

To generate a single random number from a Chi-Square Distribution with df=2 (degrees of freedom):

import numpy as np

random_number = np.random.chisquare(df=2)
print(random_number)

Output :

4.416454073420925

Example 2: Generate an Array of Random Numbers

To generate multiple random numbers:

random_numbers = np.random.chisquare(df=2, size=5)
print(random_numbers)

Output :

[0.66656494 3.55985755 1.78678662 1.53405371 4.61716372]

Visualizing the Chi-Square Distribution

Visualizing the generated numbers helps to understand the behavior of the Chi-Square distribution. You can plot a histogram or a density plot using libraries like Matplotlib and Seaborn.

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

df = 1  
size = 1000  

data = np.random.chisquare(df=df, size=size)

sns.displot(data, kind="kde", color='purple', label=f'Chi-Square (df={df})')

plt.title(f"Chi-Square Distribution (df={df})")
plt.xlabel("Value")
plt.ylabel("Density")
plt.legend()
plt.grid(True)

plt.show()

Output:

Chi-Square Distribution

The above chart shows the shape of the Chi-Square distribution for df = 1:

• The x-axis represents the values generated.
• The y-axis shows the density (how often values occur).
• With df = 1 the curve is skewed to the right meaning lower values occur more frequently and higher values become rarer.