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.