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Chi-Square Distribution

The chi-square distribution is widely used in hypothesis testing and statistical inference. It is used to measure how well an observed distribution fits an expected distribution, or in tests of independence.

Key Topics

Generating Chi-Square Distribution

NumPy's random.chisquare() function generates random numbers from a chi-square distribution. You specify the degrees of freedom and the size of the dataset.

Example

# Generating chi-square distribution
import numpy as np

# Degrees of freedom = 2, Size = 10
chi_values = np.random.chisquare(df=2, size=10)

print("Chi-square values:", chi_values)

Output

Chi-square values: [1.24 2.31 0.58 4.12 1.89 ...]

Explanation: The random.chisquare() function generates random numbers based on a chi-square distribution with 2 degrees of freedom.

Visualizing the Distribution

You can use a histogram to visualize the chi-square distribution and analyze how the degrees of freedom affect its shape.

Example

# Visualizing chi-square distribution
import seaborn as sns
import matplotlib.pyplot as plt

# Data
chi_values = np.random.chisquare(df=2, size=1000)

# Plot
sns.histplot(chi_values, kde=True, color="green")
plt.title("Chi-Square Distribution")
plt.xlabel("Value")
plt.ylabel("Frequency")
plt.show()

Output

A histogram showing the distribution of chi-square values.

Explanation: The histogram shows the chi-square distribution's skewed shape, characteristic of lower degrees of freedom.

Key Takeaways

  • Chi-Square Distribution: Used for goodness-of-fit tests and independence tests in statistics.
  • Simulation: Use random.chisquare() to generate random numbers for analysis.
  • Visualization: Histograms help identify how the degrees of freedom affect the distribution.
  • Applications: Analyze observed vs. expected frequencies and independence in categorical data.
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