Chi-Squared Probability Function (χ2)

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

  • AKA: [math]\chi^2[/math].
  • Context:
  • Example(s):
    • [math]\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...[/math]
    • [math]\chi^2(k=2,x=1) = [/math] (1 / ((2^0.5) * ((0.5 - 1) !)) * (1.0^(0.5 - 1)) * (e^(((-1) * 1.0) / 2)) = 0.24197072...
    • [math]\chi^2(k=2,x=2) = [/math] (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

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2008

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1999

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