Chi-squared Distribution

This is the gamma distribution with $L=0.0$ and $S=2.0$ and $\alpha =\nu /2$ where $\nu$ is called the degrees of freedom. If $Z_1,\dots ,Z_{\nu }$ are all standard normal distributions, then $W={\sum }_k{Z}_k^2$ has (standard) chi-square distribution with $\nu$ degrees of freedom.

The standard form has support $x\ge 0$.

where $\gamma$ is the lower incomplete gamma function, $\gamma \left(s,x\right)={\int }_0^x{t}^{s-1}{e}^{-t}dt$. For fixed $s$, ${\gamma }^{-1}\left(s,y\right)$ denotes the inverse with respect to $x$; that is, $\gamma \left(s,{\gamma }^{-1}\left(s,y\right)\right)=y$.

Implementation: scipy.stats.chi2