TheChi-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):
Pythonimportnumpyasnprandom_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:
Pythonrandom_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 likeMatplotlib and Seaborn.
Pythonimportnumpyasnpimportmatplotlib.pyplotaspltimportseabornassnsdf=1size=1000data=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 DistributionThe above chart shows theshape of the Chi-Square distribution fordf = 1:
- Thex-axis represents the values generated.
- They-axis shows thedensity (how often values occur).
- With
df = 1 the curve isskewed to the rightmeaning lower values occur more frequently and higher values become rarer.