Chi-squared Distribution

If $Z_1,Z_2\dots Z_k$ are independent from each other, then we have:

$$Q=Z_1^2+Z_2^2+\cdots +Z_k^2$$

服从自由度为$k$的 Chi-squared Distribution, which is $Q\sim {\chi }^2(k)$

The shape of the Chi-squared Distribution is highly dependent on the degree of freedom $k$, here is a graph of different pdfs of $k=1,3,6$:

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Other famous distributions:

• Student’s t-test