카이분포 (Chi Distribution)

$ x \in [ \ 0 \ , \ \infty \ ) $

$ f(x) = \frac{2^{1 - \nu/2} \cdot x^{\nu - 1} \cdot e^{-x^{2} / 2}}{\Gamma \left( \frac{1}{2} \nu \right) } $

$ F(x) = P \left( \ \frac{1}{2} \nu \ , \ \frac{1}{2} x^{2} \ \right) $

$ E(X) = \frac{\sqrt{2} \ \Gamma \left( \frac{1}{2} (\nu + 1) \right) }{\Gamma \left( \frac{1}{2} \nu \right) } $

$ Var(X) = \frac{2 \left[ \Gamma \left( \frac{1}{2} \nu \right) \cdot \Gamma \left( 1 + \frac{1}{2} \nu \right) - \Gamma^{2} \left( \frac{1}{2} (\nu + 1) \right) \right]}{\Gamma^{2} \left( \frac{1}{2} \nu \right)} $

• 분포