The chi-square distribution is a fundamental probability distribution used in hypothesis testing, particularly in chi-square tests. It’s implemented in Python’s NumPy library using the np.random.chisquare function.

Properties:

• Non-negative: The chi-square distribution applies to non-negative values (x ≥ 0).
• Shape: The shape of the distribution depends on the degrees of freedom (df) parameter. Higher degrees of freedom lead to a more symmetrical and bell-shaped curve.
• Degrees of Freedom (df): This parameter (represented by df in the function) influences the shape of the distribution. It relates to the number of independent squared standard normal variables used to generate the chi-square variate.

Applications:

• Chi-Square Tests: Hypothesis testing in statistics to assess the fit between observed data and a theoretical distribution or compare proportions across categories.

Generating Random Samples with np.random.chisquare:

import numpy as np

# Generate 10 random samples with degrees of freedom 5
samples = np.random.chisquare(df=5, size=10)
print(samples)

Parameters:

• df (float or array-like of floats): The degrees of freedom parameter (must be > 0).
• size (int or tuple of ints, optional): The desired output shape. If left as None (default), it returns a single value if df is a scalar, otherwise an array with the same shape as df.

Important Note: While np.random.chisquare generates samples from the chi-square distribution, it’s essential to use this within the context of chi-square tests and understand the statistical assumptions behind it.