# Chi-Squared Probability Function (χ2)

(Redirected from Chi Square Distribution)

A Chi-Squared Probability Function (χ2) is the Gamma probability function from a Chi-squared distribution family (based on a sum of squares of $k$ independent standard normal random variables).

• AKA: $\chi^2$.
• Context:
• Example(s):
• $\chi^2(k=2,x=0.5) = \frac{1}{2^{0.5} \times (0.5 - 1)!) \times (0.5^{(0.5 - 1)}) \times (e^{(((-1) * 0.5) / 2)}} = 0.43939129...$
• $\chi^2(k=2,x=1) =$ (1 / ((2^0.5) * ((0.5 - 1) !)) * (1.0^(0.5 - 1)) * (e^(((-1) * 1.0) / 2)) = 0.24197072...
• $\chi^2(k=2,x=2) =$ (1 / ((2^0.5) * ((0.5 - 1) !)) * (2.0^(0.5 - 1)) * (e^(((-1) * 2.0) / 2)) = 0.10377687...
• Counter-Example(s):
• See: Chi-Squared Test.

## References

### 1999

• (Lane, 1999) ⇒ D. Lane. (1999). “HyperStat Online Textbook". Chapter 16: Chi Square.