Definition:Chi Distribution

Definition

Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $\Img X = \hointr 0 \infty$.

Let $r$ be a strictly positive integer.

$X$ is said to have a chi distribution with $r$ degrees of freedom if and only if it has probability density function:

$\map {f_X} x = \dfrac 1 {2^{\paren {r / 2} - 1} \map \Gamma {r / 2} } x^{r - 1} e^{- x^2 / 2}$

where $\Gamma$ denotes the gamma function.

This is written:

$X \sim \chi_r$

Also see

• Results about the chi distribution can be found here.

Sources

• Weisstein, Eric W. "Chi Distribution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChiDistribution.html