Chi-Square 5

Data Science Day 7:

Where does the name of Chi-square distribution come from?

From the first day, we know Chi-square distribution is the sum of the squared standard deviates, known as variance.

If we investigate the standard deviates, then we find an interesting relation between Chi-square and Normal Distribution:

If a variable follows the standard normal distribution, then its square follows the Chi-square distribution.

Data Visualization:

  • We first generate 1000 random normal variables and use the histogram graph to show their distribution. We see it approaches a normal distribution.

Normal Distribution of a Random Variable

  • We square the random normal variables and plot the values. We see it approaches a Chi-square distribution.  This graph is one random variable squared, so we will show another distribution with a higher degree.

Chi-square Distribution of the Random Number Square with degree 1

  •  We use the square of three normal random variables and we can see the  graph indeed follows Chi-square distribution.

Chi-square distribution of random variable square with degree 3

 

Source code

Thanks very much to Jie Chen, she helped me to understand the connection between the Normal and Chi-Square Distribution.

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